Exploring Distance and Midpoint Concepts

What is the purpose of the distance formula in coordinate geometry?

• To find the midpoint between two points

• To calculate the slope of a line

• To determine the distance between two points

• To find the area of a triangle

In the distance formula, what does the expression (x2 - x1)^2 represent?

• The sum of y-coordinates squared

• The sum of x-coordinates squared

• The difference in x-coordinates squared

• The difference in y-coordinates squared

Given points A(0, 3) and B(0, 12), what is the distance between them?

• 9

• 3

• 12

• 15

If point A is at (6, -2) and point B is at (-2, 4), what is the distance between them?

• 12

• 10

• 14

• 8

What is the midpoint formula used for?

• To find the area of a rectangle

• To find the point exactly in the middle between two points

• To find the distance between two points

• To find the slope of a line

Given points A(2, 4) and B(6, 10), what is the midpoint?

• (5, 8)

• (3, 5)

• (4, 7)

• (4, 6)

For points A(-3, 7) and B(2, -1), what is the midpoint?

• (-0.5, 3)

• (0.5, 3)

• (-0.5, 4)

• (0.5, 4)

Given an endpoint A(4, 7) and a midpoint M(8, 10), what is the other endpoint B?

• (16, 17)

• (14, 15)

• (10, 12)

• (12, 13)

If the midpoint is (5, 12) and one endpoint is (2, 6), what is the other endpoint?

• (8, 18)

• (7, 16)

• (9, 20)

• (6, 14)

What is the first step in finding the unknown endpoint when given a midpoint and one endpoint?

• Multiply the midpoint coordinates by 2

• Add the coordinates of the known endpoint

• Subtract the known endpoint coordinates from the midpoint

• Divide the midpoint coordinates by 2