Question

A segment has an endpoint at (1,−2). The midpoint is at (−4,−2). What are the coordinates of the other endpoint?

(−1.5,−2)

(−9,−2)

(6,−2)

(−8,−2)

Answer 1

The other midpoint is located at coordinates (-9,-2) (Second option)

Explanation:

Midpoints

If P(a,b) and Q(c,d) are points in
`\mathbb{R} ^2`, the midpoint between them is the point exactly in the center of the line that joins P and Q. Its coordinates are given by

`\displaystyle x_m=(a+c)/(2)`

`\displaystyle y_m=(b+d)/(2)`

We are given one endpoint at P(1,-2) and the midpoint at M(-4,-2). The other endpoint must be at an equal distance from the midpoint as it is from P. We can see both given points have the same value of y=-2. This simplifies the calculations because we only need to deal with the x-coordinate.

The x-distance from P to M is 1-(-4)=5 units. This means the other endpoint must be 5 units to the left of M:

x (other endpoint)= - 4 - 5 = - 9

So the other midpoint is located at (-9,-2) (Second option)