Question

find the missing endpoint given point a and midpoint m

1. a(2, 5) and m(3, 4)

Explanation:

Step1: Recall mid - point formula

The mid - point formula between 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 $A(x_1,y_1)=(2,5)$ and $M(x_m,y_m)=(3,4)$, and the missing endpoint be $B(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $3=\frac{2 + x_2}{2}$. Cross - multiply: $3\times2=2 + x_2$, so $6 = 2+x_2$. Then $x_2=6 - 2=4$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $4=\frac{5 + y_2}{2}$. Cross - multiply: $4\times2=5 + y_2$, so $8 = 5+y_2$. Then $y_2=8 - 5=3$.

Answer:

$(4,3)$