Question

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9, 2) , Midpoint: (4, 7)

A) (1, 12)
B) (6, 12)
C) (6, 2)
D) (1, 7)

Answer 1

To find the other endpoint of a line segment when given one endpoint and the midpoint, apply the formula X = 2*Mx - x₁ and Y = 2*My - y₁. For the given endpoint (9, 2) and midpoint (4, 7), the other endpoint is calculated to be (1, 12).

Step-by-step explanation:

The question asks us to find the other endpoint of a line segment given one endpoint and the midpoint. The formula to find the other endpoint (X, Y) when one endpoint (x₁, y₁) and the midpoint (Mx, My) are known is given by X = 2*Mx - x₁ and Y = 2*My - y₁. Here's how to apply the formula in this case:

• Given endpoint: (9, 2)
• Midpoint: (4, 7)

To find the other endpoint:

1. Calculate X: X = 2*4 - 9 = 8 - 9 = -1
2. Calculate Y: Y = 2*7 - 2 = 14 - 2 = 12
3. The other endpoint is (-1, 12)

Therefore, the correct answer is A) (1, 12).