Question

1. in the standard (x,y) coordinate plane, the midpoint of $overline{ab}$ is at (2,1), and a is at (8,10). what is the x - coordinate of b?

a. - 4
b. - 6
c. - 8
d. 3
e. 5

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A=(x_1,y_1)=(8,10)$ and $B=(x_2,y_2)$, and the mid - point $M=(2,1)$. We only care about the $x$ - coordinates, so we use the $x$ - coordinate part of the mid - point formula $\frac{x_1 + x_2}{2}$.

Step2: Substitute values into formula

We know that $\frac{x_1 + x_2}{2}=2$ and $x_1 = 8$. Substituting $x_1$ into the formula gives $\frac{8 + x_2}{2}=2$.

Step3: Solve for $x_2$

Multiply both sides of the equation $\frac{8 + x_2}{2}=2$ by 2: $8 + x_2=4$. Then subtract 8 from both sides: $x_2=4 - 8=-4$.

Answer:

A. -4