Question

Y is the midpoint of XZ. Find the coordinates of X.Z(-6, 5), Y(0,2)

Answer 1

Answer:

X (6, 2)

Explanations:

If the midpoint of a line having endpoints (x₁, y₁) and (x₂, y₂) is represented by (a, b), then the coordinates of the midpoints a and b can be calculated using the formulae:

$\begin{gathered} a\text{ = }\frac{x_1+x_2}{2} \\ b\text{ = }\frac{y_1+y_2}{2} \end{gathered}$

In the line described in this question, Y(0,2) is the midpoint. X and Z are the endpoints

This can be illustrated using the line below

$\begin{gathered} a=0,b=2,x_2=-6,y_2=5 \\ a\text{ = }\frac{x_1+x_2}{2} \\ 0\text{ = }\frac{x_1+(-6)}{2} \\ 0=x_1-6 \\ x_1=6 \\ b\text{ = }\frac{y_1+y_2}{2} \\ 2\text{ = }\frac{y_1+2}{2} \\ 4=y_1+2 \\ y_1=4\text{ - 2} \\ y_1=2 \end{gathered}$

The coordinates of X are (6, 2)