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Quizzes > High School Quizzes > Mathematics

Distance in Coordinate Plane Practice Quiz

Conquer worksheet challenges with engaging quiz questions

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art representing a trivia quiz on Coordinate Distance Quest for high school students.

What is the distance between the points (0, 0) and (3, 4)?
6
4
7
5
By applying the distance formula, we compute the distance as √[(3-0)² + (4-0)²] = √(9+16) = √25 = 5. Therefore, 5 is the correct answer.
Find the distance between the points (1, 2) and (1, 5).
2
4
5
3
Since the x-coordinates are the same, the distance is simply the absolute difference between the y-coordinates: |5-2| = 3. This makes 3 the correct answer.
Calculate the distance between the points (-2, 1) and (1, 1).
2
4
5
3
Because the points have identical y-values, the distance is the absolute difference of their x-values: |1 - (-2)| = 3. Hence, the correct distance is 3.
Determine the distance between the points (2, 3) and (2, -1).
2
4
3
5
With identical x-coordinates, the distance comes from the difference in y-coordinates: |3 - (-1)| = 4. This confirms that 4 is the correct answer.
What is the distance from (5, 5) to (5, 5)?
1
10
0
5
Since both points are identical, there is no separation between them. The distance is therefore 0, which is the correct answer.
Find the distance between (2, -3) and (7, 1).
√40
√45
√41
√35
Using the distance formula, we calculate dx = 7-2 = 5 and dy = 1-(-3) = 4. The distance is √(5² + 4²) = √(25+16) = √41, making √41 the correct answer.
What is the distance between the points (-1, -1) and (2, 3)?
4
6
5
7
The differences between the coordinates are 3 and 4, respectively. Applying the formula gives √(3² + 4²) = √(9+16) = √25, which equals 5.
Calculate the distance between the points (4, 0) and (-2, 0).
4
8
6
2
Since the y-coordinates are identical, the distance is the absolute difference in the x-coordinates: |4 - (-2)| = 6. Hence, 6 is the correct distance.
Determine the distance between (0, -3) and (4, 1).
2√2
4√2
√20
√34
The x and y differences are both 4, so the distance is √(4² + 4²) = √(16+16) = √32, which simplifies to 4√2. Therefore, 4√2 is the correct answer.
What is the distance between the points (3,5) and (3,-2)?
7
6
5
8
With the x-coordinates the same, the distance is found by the difference in y-coordinates: |5 - (-2)| = 7. This makes 7 the correct answer.
Find the distance between (-3, -4) and (0, 0).
5
7
6
8
Computing the differences gives 3 and 4, and by the distance formula the result is √(3² + 4²) = √(9+16) = √25 = 5. Thus, 5 is the correct distance.
Calculate the distance between the points (5, 2) and (2, 6).
6
5
4
7
The differences in the coordinates are |5-2| = 3 and |2-6| = 4. Applying the distance formula gives √(3² + 4²) = √(9+16) = √25 = 5.
What is the distance from (-1, 4) to (2, -2)?
2√5
3√5
√50
√41
Using the distance formula, we get dx = 2 - (-1) = 3 and dy = -2 - 4 = -6. The distance is √(3² + (-6)²) = √(9+36) = √45, which simplifies to 3√5.
Find the distance between the points (6, -3) and (-2, 5).
8√2
16
√100
10
The differences are dx = -2 - 6 = -8 and dy = 5 - (-3) = 8, so the distance is √((-8)² + 8²) = √(64+64) = √128, which simplifies to 8√2. This verifies the correct answer.
Determine the distance between (1, -1) and (-4, 3).
√25
√41
√34
5
Calculating the differences gives dx = -4 - 1 = -5 and dy = 3 - (-1) = 4, leading to the distance √(5² + 4²) = √(25+16) = √41. Thus, √41 is the correct answer.
Given the points (1, 3) and (4, b) are 5 units apart and b > 3, what is the value of b?
7
9
5
-1
Using the distance formula, we set up the equation √[(4-1)² + (b-3)²] = 5, which simplifies to √(9 + (b-3)²) = 5. Squaring both sides gives 9 + (b-3)² = 25, so (b-3)² = 16, yielding b = 3 ± 4. With b > 3, the correct value is 7.
The coordinates of two points are given as (x, 2) and (5, 6) with a distance of 5 units. If x < 5, what is the value of x?
2
8
3
4
Applying the distance formula, we have √[(5-x)² + (6-2)²] = 5, which leads to (5-x)² + 16 = 25. Solving gives (5-x)² = 9 so x = 5 ± 3. Since x must be less than 5, x = 2 is the correct answer.
Find the distance between the midpoints of the segments with endpoints (1, 2) & (5, 6) and endpoints (-2, 3) & (2, -1).
4√2
3√3
3√2
5
The midpoint of (1, 2) and (5, 6) is (3, 4), and that of (-2, 3) and (2, -1) is (0, 1). The distance between these midpoints is √[(3-0)² + (4-1)²] = √(9+9) = √18, which simplifies to 3√2.
If the distance between (1, y) and (7, 8) is 10 units and y < 8, what is the value of y?
0
16
10
8
Setting up the equation √[(7-1)² + (8-y)²] = 10 results in √(36+ (8-y)²) = 10. Squaring both sides gives 36 + (8-y)² = 100, so (8-y)² = 64. This leads to y = 8 ± 8; with the condition y < 8, y must be 0.
Two points A(2, k) and B(-3, 7) are √58 units apart. If k < 7, what is the value of k?
7 - √33
7 + √33
33/7
√33 - 7
The distance between A and B is given by √[(-3-2)² + (7-k)²] = √[25 + (7-k)²] = √58. Squaring both sides gives 25 + (7-k)² = 58, so (7-k)² = 33. Taking the square root yields 7-k = √33 or -√33; with k < 7, we choose 7-k = √33, which gives k = 7 - √33.
0
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Study Outcomes

  1. Apply the distance formula to calculate the distance between two points on the coordinate plane.
  2. Analyze coordinate graphs to identify key points and their relationships.
  3. Interpret problem scenarios to formulate strategies using coordinate geometry principles.
  4. Simplify algebraic expressions arising from the application of the distance formula.
  5. Evaluate and verify solutions by checking consistency with geometric properties.

Distance in Coordinate Plane Worksheet Cheat Sheet

  1. Master the Distance Formula - Ready to be a geometry wizard? Plug your points into d = √((x₂ − x₝)² + (y₂ − y₝)²) and watch distances pop up effortlessly. This is your golden ticket to measuring gaps on any coordinate plane. Distance Formula Practice
  2. Connect to the Pythagorean Theorem - Think of the distance formula as a Pythagorean theorem remix: the differences in x and y form the legs of a right triangle. When you square, add, and root, you're just finding the hypotenuse. Embrace this link and your formula skills will skyrocket. Interactive Explanation
  3. Tackle Real-World Scenarios - Geometry isn't just on paper - use the distance formula to map the shortest route between two landmarks or to plan an epic road trip. Applying math to real life cements your understanding and makes study sessions more exciting. Real-World Problems
  4. Calculate Midpoints Accurately - Splitting a line segment in half? Compute ((x₝ + x₂)/2, (y₝ + y₂)/2) to find the exact center. Midpoints help you bisect segments, create symmetry, and solve countless geometry puzzles. Midpoint Drills
  5. Find Point-to-Line Distance - Curious about the shortest drop from a point to a line Ax + By + C = 0? Use |Ax₀ + By₀ + C| / √(A² + B²) and voilà - you've got that perpendicular measure. Perfect for engineering and design applications. Point‑to‑Line Calculator
  6. Measure Distance Between Parallel Lines - Given Ax + By + C₝ = 0 and Ax + By + C₂ = 0, compute |C₝ − C₂| / √(A² + B²) to see how far apart they run. This builds intuition for spacing in tiling, architecture, and more. Parallel Lines Guide
  7. Extend to Three Dimensions - Jump into 3D space with d = √((x₂−x₝)² + (y₂−y₝)² + (z₂−z₝)²). Visualize points in cubes and boxes, and you'll master 3D modeling, physics, and game design fundamentals. 3D Distance Practice
  8. Solve Practice Problems - The more you solve, the sharper you get! Try finding distances between (-1,2) and (2,3), or design your own challenges. Regular drills cement formulas into muscle memory. Practice Drills
  9. Visualize with Graphs - Sketch your points, draw the connecting segment, and label the legs of your triangle. Seeing the geometry in action turns abstract numbers into a clear picture. Graphical Worksheet
  10. Verify and Check Your Work - Always plug your results back into the formula to avoid sneakily misplaced negatives or typos. Consistent checking builds confidence - and turns you into a geometry pro! Self-Check Practice
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