Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > Mathematics > Geometry

Put Your Distance and Midpoint Formula to the Test!

Ready for midpoint questions and distance formula practice? Dive in!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art design with two points connected by line midpoint mark distance formula text on dark blue background

Ready to sharpen your geometry know-how? Our Distance & Midpoint Formula Quiz is designed to test your skills on the formula for distance and midpoint while offering targeted skills practice distance and midpoints. Whether you're tackling midpoint questions for the first time or seeking additional practice midpoint and distance challenges, this free quiz delivers a rapid, fun way to level up. Plus, you'll get instant feedback on each question to pinpoint improvement areas. Dive into distance formula practice problems to see real-world applications, and explore distance and displacement practice that reinforces concepts. Are you up for the challenge? Start now to boost your math skills and track your progress!

What is the distance between points (0,0) and (3,4)?
4
5
6
7
Using the distance formula d = ?[(x? - x?)² + (y? - y?)²], we calculate ?[(3-0)² + (4-0)²] = ?(9 + 16) = ?25 = 5. The result shows the direct straight-line distance between the two points. Learn more about the distance formula.
What is the midpoint of (2,2) and (4,4)?
(1,1)
(2,4)
(3,3)
(4,2)
The midpoint formula is ((x? + x?)/2, (y? + y?)/2). Substituting gives ((2+4)/2, (2+4)/2) = (3,3). This point lies exactly halfway between the two given points. Learn more about midpoints.
What is the distance between (1,2) and (1,5)?
?10
4
?13
3
Since the x-coordinates are the same, distance is simply |y? - y?| = |5 - 2| = 3. This is a vertical line segment. More on vertical/horizontal distances.
What is the midpoint of (-1,-1) and (1,1)?
(-1,1)
(2,2)
(1,-1)
(0,0)
Midpoint = ((-1+1)/2, (-1+1)/2) = (0/2,0/2) = (0,0). This is the center point of the segment connecting the two points. Midpoint concept.
Calculate the distance between (5,0) and (5,12).
7
13
5
12
The x-coordinates match, so distance = |12 - 0| = 12. This vertical segment measures 12 units. Vertical/horizontal distance.
What is the midpoint of (0,10) and (0,0)?
(5,0)
(5,5)
(0,5)
(0,10)
Midpoint formula gives ((0+0)/2, (10+0)/2) = (0,5). It divides the vertical segment into equal halves. Midpoint details.
Find the distance between (2,3) and (6,3).
4
6
3
5
Since y-coordinates are the same, distance = |6 - 2| = 4. Horizontal segments use the difference in x-values. Distance formula review.
What is the midpoint of (7,3) and (3,1)?
(7,1)
(4,2)
(3,3)
(5,2)
Calculate ((7+3)/2, (3+1)/2) = (5,2). This point balances both x and y coordinates. Midpoint examples.
What is the distance between (-2,4) and (3,-1)?
5?2
10
?10
2?5
Compute differences: ?x=5, ?y=?5, so d=?(5² + (?5)²)=?(25+25)=?50=5?2. This uses the full distance formula. Distance formula details.
Which formula gives the midpoint of (x?,y?) and (x?,y?)?
((x??x?)/2, (y??y?)/2)
(x?+x?, y?+y?)
((x??x?)/2, (y??y?)/2)
((x?+x?)/2, (y?+y?)/2)
The midpoint formula averages each coordinate: ((x?+x?)/2,(y?+y?)/2). This finds the exact center point. Midpoint formula explained.
Distance between (?3,0) and (0,?3)?
2?3
?6
3
6
Compute ?x=??3, ?y=?3, so d=?[(?3)²+(?3)²]=?(3+3)=?6. The radical simplifies accordingly. Radical distances.
What is the midpoint of (-4,5) and (2,-3)?
(0,2)
(-1,1)
(-2,4)
(1,-1)
Midpoint = ((-4+2)/2, (5+(-3))/2) = (-2/2, 2/2) = (-1,1). This balances both coordinates evenly. Midpoint calculation.
Compute the distance between (1/2, 1/2) and (3/2, 5/2).
3
2
?5
?10
?x=1, ?y=2, so d=?(1²+2²)=?5. Fractions cancel nicely in the subtraction. Fraction distances.
The midpoint of (a,b) and (a,-b) is:
(0,b)
(a,0)
(a,b)
(2a,0)
Midpoint = ((a+a)/2, (b+(-b))/2) = (a, 0). The y-values cancel each other, landing at zero. Midpoint algebraic.
Find the distance between (2,-1) and (-3,4).
6
7
?29
5?2
?x = -5, ?y = 5, so d = ?(25 + 25) = ?50 = 5?2. Both coordinate changes are equal in magnitude. Distance with negatives.
What is the midpoint of (10,-2) and (-4,8)?
(2,3)
(8,4)
(6,6)
(3,3)
Midpoint = ((10 + (?4))/2, (?2 + 8)/2) = (6/2, 6/2) = (3, 3). This equally splits both axes. Midpoint with negatives.
If the midpoint of A(x?,y?) and B(x?,y?) is (4,?2) and A is (2,1), what are the coordinates of B?
(5,?2)
(2,?5)
(8,?3)
(6,?5)
We use 4 = (2 + x?)/2 so x? = 6, and ?2 = (1 + y?)/2 so y? = ?5. Thus B is (6,?5). Midpoint reverse solve.
Find the distance between complex points 3+4i and ?1+2i.
?17
?20
2?5
5
Subtract as vectors: (3 - (?1)) + (4 - 2)i = 4 + 2i, then magnitude = ?(4²+2²)=?20=2?5. Complex distance.
Point P divides the segment from (0,0) to (8,6) in the ratio 1:3. What are P's coordinates?
(4,3)
(6,4.5)
(1,0.75)
(2,1.5)
Section formula: x = (1·8 + 3·0)/(1+3)=2, y = (1·6 + 3·0)/4=1.5. P is closer to the first endpoint. Section formula.
Endpoints of a diameter are (?2,1) and (4,7). What is the circle's center and radius?
Center (2,3), radius 3
Center (1,4), radius 6?2
Center (1,4), radius 3?2
Center (1,4), radius 6
Center is midpoint = ((?2+4)/2,(1+7)/2)=(1,4). Diameter length = ?[(6)²+(6)²]=6?2 so radius = half = 3?2. Circle properties.
Are segments AB and BC equal if A(1,2), B(4,6), C(7,2)?
No, BC is longer
They are equal only if the triangle is right
Yes, both have length 5
No, AB is longer
Compute AB = ?[(4-1)²+(6-2)²]=?(9+16)=5 and BC = ?[(7-4)²+(2-6)²]=?(9+16)=5. Both segments are equal. Distance examples.
Find the centroid of triangle with vertices (0,0), (4,0), (4,3).
(4/3,1)
(2,1)
(8/3,1)
(3,1)
Centroid = average of x's and y's: ((0+4+4)/3, (0+0+3)/3) = (8/3,1). It's the triangle's balance point. Centroid formula.
In a right triangle, what point is equidistant from all three vertices?
Orthocenter
Centroid
Incenter
Midpoint of the hypotenuse
In a right triangle, the midpoint of the hypotenuse is equidistant from all three vertices because the hypotenuse is a diameter of its circumcircle. Right triangle circumcenter.
What is the equation of the perpendicular bisector of the segment joining A(-1,3) and B(4,-2)?
y = -x - 1
y = x + 1
y = x - 1
y = -x + 1
Midpoint M = ((-1+4)/2, (3+(-2))/2) = (1.5,0.5). Slope AB = (-2-3)/(4+1) = -1, so perp slope = 1. Equation: y-0.5 =1(x-1.5) ? y = x - 1. Perpendicular bisector.
Which formula gives the coordinates of a point P dividing segment AB (A(x?,y?), B(x?,y?)) in ratio k:1 internally?
((x? + kx?)/(k-1), (y? + ky?)/(k-1))
((x? + kx?)/(k+1), (y? + ky?)/(k+1))
((kx? + x?)/(k+1), (ky? + y?)/(k+1))
((x? + kx?)/(k+1), (y? + ky?)/(k+1))
Internal section formula: P = ((x? + kx?)/(1+k), (y? + ky?)/(1+k)). It weights the coordinates by the given ratio. Section formula details.
0
{"name":"What is the distance between points (0,0) and (3,4)?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"What is the distance between points (0,0) and (3,4)?, What is the midpoint of (2,2) and (4,4)?, What is the distance between (1,2) and (1,5)?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Understand the formula for distance and midpoint -

    Gain a clear grasp of how to calculate distances between two points and locate their midpoint using the formula for distance and midpoint.

  2. Apply the distance formula to solve real-world problems -

    Use the distance formula to tackle practical scenarios, enhancing your ability to measure lengths on the coordinate plane.

  3. Compute midpoints in various midpoint questions -

    Master midpoint questions by accurately finding the central point between pairs of coordinates.

  4. Complete 1-3 additional practice midpoint and distance exercises -

    Reinforce your understanding with targeted problems designed to solidify both distance and midpoint concepts.

  5. Analyze coordinate geometry scenarios -

    Interpret spatial relationships by examining points on the Cartesian plane and determining key measurements.

  6. Engage in 1-3 skills practice distance and midpoints -

    Boost your proficiency through dedicated challenges that blend midpoint questions with distance calculations.

  7. Build confidence in tackling distance and midpoint challenges -

    Develop self-assurance in your math skills by practicing and reviewing solutions to distance and midpoints problems.

Cheat Sheet

  1. Distance Formula Essentials -

    The distance formula d = √[(x₂ - x₝)² + (y₂ - y₝)²] comes directly from the Pythagorean theorem, letting you calculate the straight-line distance between any two points. For example, between (1,2) and (4,6), d = √[(4 - 1)² + (6 - 2)²] = 5. A handy mnemonic is "D = √I² + C²" (leg lengths I and C) to recall the structure quickly (source: MIT OpenCourseWare).

  2. Midpoint Formula Fundamentals -

    The midpoint formula M = ((x₝ + x₂)/2, (y₝ + y₂)/2) finds the exact center of a segment in the plane. For points (2,3) and (8,7), M = (5,5), ensuring each half is congruent. Remember "add then halve" to lock in the process (source: Cornell University Math).

  3. Interplay of Distance & Midpoint -

    Understanding how the formula for distance and midpoint interrelate helps tackle midpoint questions by first confirming equal segment lengths. If the distances from an endpoint to your computed midpoint match, you know your midpoint is correct. This dual-check strategy is widely used in physics and engineering problem sets (source: Harvard Math Department).

  4. Targeted Practice Sessions -

    Boost your confidence with 1-3 additional practice midpoint and distance exercises that span all four quadrants. Try problems like finding the midpoint and distance for ( - 3,4) and (5, - 2) to master handling negative coordinates. Regular drills from reputable platforms such as Math StackExchange or AoPS cement your understanding.

  5. Real-World Applications -

    Distance and midpoint formulas underpin key tasks in navigation, computer graphics, and GIS mapping. Route planning uses distance calculations, while midpoint finds center points for rendering and spatial analyses. Seeing these real-world links makes the formulas more engaging and memorable (source: National Institute of Standards and Technology).

Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Geometry Quizzes

Powered by: Quiz Maker