Question

7 if a line segment has endpoints a(3x + 5,3y) and b(x - 1,-y), what are the coordinates of the midpoint of $overline{ab}$? 1) (x + 3,2y) 2) (2x + 2,y) 3) (2x + 3,y) 4) (4x + 4,2y)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=3x + 5$, $y_1 = 3y$, $x_2=x - 1$, $y_2=-y$.

Step2: Calculate the x - coordinate of the mid - point

$\frac{(3x + 5)+(x - 1)}{2}=\frac{3x+5+x - 1}{2}=\frac{4x + 4}{2}=2x+2$.

Step3: Calculate the y - coordinate of the mid - point

$\frac{3y+( - y)}{2}=\frac{3y - y}{2}=\frac{2y}{2}=y$.

Answer:

1. $(2x + 2,y)$