Question

in exercises 17 - 20, the mid - point m and one endpoint of gh are given. find the coordinates of the other endpoint.
17 g(5, 6) and m(4, 3)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $G(x_1,y_1)=(5,6)$ and $M(x_m,y_m)=(4,3)$, and the other endpoint be $H(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $4=\frac{5 + x_2}{2}$. Cross - multiply: $4\times2=5 + x_2$, so $8 = 5+x_2$. Then $x_2=8 - 5=3$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $3=\frac{6 + y_2}{2}$. Cross - multiply: $3\times2=6 + y_2$, so $6 = 6+y_2$. Then $y_2=6 - 6=0$.

Answer:

$(3,0)$