Question

find the coordinates of x if m(-3,-1) is the midpoint of xy and y has coordinates of (-8,6). a line segment on the coordinate plane has endpoints (-2,7) and (5,y). the midpoint of the segment is point (1.5,1). what is the value of y?

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Find the x - coordinate of X in the first problem

Let the coordinates of $X$ be $(x,y)$. Given $M(-3,-1)$ is the mid - point of $XY$ where $Y(-8,6)$. For the x - coordinate: $\frac{x+( - 8)}{2}=-3$. Multiply both sides by 2: $x - 8=-6$. Add 8 to both sides: $x = 2$.

Step3: Find the y - coordinate of X in the first problem

For the y - coordinate: $\frac{y + 6}{2}=-1$. Multiply both sides by 2: $y+6=-2$. Subtract 6 from both sides: $y=-8$. So the coordinates of $X$ are $(2,-8)$.

Step4: Find the value of y in the second problem

Given endpoints $(-2,7)$ and $(5,y)$ and mid - point $(1.5,1)$. For the y - coordinate of the mid - point: $\frac{7 + y}{2}=1$. Multiply both sides by 2: $7 + y = 2$. Subtract 7 from both sides: $y=-5$.

Answer:

The coordinates of $X$ are $(2,-8)$ and the value of $y$ is $-5$.