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 $A(x_1,y_1)$ and $B(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A(2,5)$ with $x_1 = 2,y_1 = 5$ and $M(3,4)$ with $x_M=3,y_M = 4$.

Step2: Find the x - coordinate of the missing point

We know that $x_M=\frac{x_1 + x_2}{2}$. Substituting the known values: $3=\frac{2 + x_2}{2}$. Cross - multiply: $3\times2=2 + x_2$. Then $6=2 + x_2$. Solving for $x_2$ gives $x_2=6 - 2=4$.

Step3: Find the y - coordinate of the missing point

We know that $y_M=\frac{y_1 + y_2}{2}$. Substituting the known values: $4=\frac{5 + y_2}{2}$. Cross - multiply: $4\times2=5 + y_2$. Then $8=5 + y_2$. Solving for $y_2$ gives $y_2=8 - 5=3$. So the missing endpoint $B$ is $(4,3)$.

Answer:

$(4,3)$