Question

given a(2,3) and b(8,15), find the coordinates of the midpoint m and prove that m lies on the line y = 2x - 1. m(5,9), 9 = 2×5 - 1 m(5,9), 9 = 2×5 + 1 m(4,8), 8 = 2×4 - 1 m(5,8), 8 = 2×5 - 1

Explanation:

Step1: Calculate mid - point coordinates

The mid - point formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $A(2,3)$ and $B(8,15)$, we have $x=\frac{2 + 8}{2}=5$ and $y=\frac{3+15}{2}=9$, so $M(5,9)$.

Step2: Check if the point lies on the line

Substitute $x = 5$ and $y = 9$ into the line equation $y=2x - 1$. The left - hand side is $y = 9$, and the right - hand side is $2\times5-1=10 - 1=9$. Since the left - hand side equals the right - hand side, the point $M$ lies on the line.

Answer:

A. M(5,9), 9 = 2×5−1