Question

On a map, the endpoints of a straight fence are located at A(4,12) and B(8,22). Lisa plans to install a gate in the fence and wants the gate’s hinges to be the same distance from both ends of the fence. At what point on the map will the gate hinges be placed?

Answer 1

Answer:

$(6,17)$

Step-by-step explanation:

we know that

In this problem

The gate hinges must be placed at the mid-point of the fence.

The formula to calculate the midpoint between two points is

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

$A(4,12),B(8,22)$

substitute the values in the formula

$M(\frac{4+8}{2},\frac{12+22}{2})$

$M(6,17)$