The point (3, 4) has both positive x and y coordinates, which places it in the First Quadrant. In the coordinate plane, the first quadrant is where both x and y are positive.

An ordered pair is written as (x, y), so with x = -2 and y = 5, the correct written form is (-2, 5). This order matters as it distinguishes the horizontal and vertical coordinates.

The point (0, -7) lies on the y-axis because the x-coordinate is 0, and any point with an x-coordinate of 0 lies on the y-axis. This is a fundamental property of the coordinate plane.

The origin is the point where the x-axis and y-axis intersect, which is (0, 0). This is one of the first concepts learned when studying the coordinate plane.

In an ordered pair (x, y), the x-coordinate indicates the horizontal position. This tells you how far left or right a point is from the origin.

The point (-3, 4) has a negative x-coordinate and a positive y-coordinate, placing it in the Second Quadrant. Understanding the signs of coordinates aids in identifying the correct quadrant.

In the third quadrant, both coordinates are negative. (-2, -5) is the only option with both x and y negative. This property is essential in recognizing the correct quadrant.

The midpoint of a segment is found by averaging the x-coordinates and the y-coordinates separately. In this case, (2+8)/2 = 5 and (3+11)/2 = 7, so the midpoint is (5, 7).

Since the x-coordinates are the same, the distance is simply the absolute difference between the y-coordinates. Thus, |8 - 2| = 6 units.

When reflecting a point over the x-axis, the x-coordinate remains unchanged while the y-coordinate changes sign. Therefore, the reflection of (4, -3) is (4, 3).

Substituting x = 3 into the equation y = 2x + 1 gives y = 2(3) + 1 = 7. This is a straightforward application of evaluating a linear function.

Adding the x-coordinate (-4) and the y-coordinate (9) produces -4 + 9 = 5. This operation tests basic arithmetic with signed numbers.

The slope is calculated by dividing the change in y by the change in x: (5 - 0)/(2 - 0) = 5/2. This formula is fundamental in coordinate geometry.

The midpoint is found by averaging the corresponding coordinates: (0+6)/2 = 3 and (0+(-4))/2 = -2, so the midpoint is (3, -2). This confirms your understanding of the midpoint formula.

Quadrant I consists of points with both positive x and y coordinates. (-3, 4) is not in quadrant I, as its x-coordinate is negative, placing it in quadrant II.

Using the distance formula, the distance is calculated as √[(2 - (-3))² + (-1 - 3)²] = √(5² + (-4)²) = √(25 + 16) = √41. This formula is a direct application of the Pythagorean theorem.

The slope is found by dividing the difference in y-values by the difference in x-values. In this case, (3 - (-3))/(4 - (-2)) equals 6/6, which simplifies to 1.

Plugging each point into the circle's equation (x - 2)² + (y - 3)² = 25 shows that (6, 7) does not satisfy the equation, so it cannot lie on the circle. This exercise checks understanding of the circle equation.

Parallel lines have identical slopes. Since the slope of y = 3x - 5 is 3, the line y = 3x + 4 is parallel, having the same slope. This demonstrates understanding of the relationship between lines.

A translation moves a point by adding a constant vector to it. The vector (-6, 7) takes (5, -3) to (-1, 4), which is the correct transformation. This problem tests understanding of translation vectors.