Question

dorian draws a line segment on a coordinate plane with endpoints j(-2, -5) and k(6, -10). he plots point l at (1, -7) and states that it is the midpoint of $overline{jk}$. is this true? explain you must support your answer with evidence, but using the graph is optional.

Explanation:

Step1: Recall mid - point formula

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

Step2: Identify coordinates of endpoints

For points $J(-2,-5)$ and $K(6,-10)$, $x_1=-2,y_1 = - 5,x_2=6,y_2=-10$.

Step3: Calculate x - coordinate of mid - point

$x=\frac{-2 + 6}{2}=\frac{4}{2}=2$.

Step4: Calculate y - coordinate of mid - point

$y=\frac{-5+( - 10)}{2}=\frac{-5 - 10}{2}=\frac{-15}{2}=-7.5$.
The mid - point of $\overline{JK}$ is $(2,-7.5)$. Since the given point $L$ is $(1,-7)$ which is not equal to $(2,-7.5)$.

Answer:

No. The mid - point of the line segment with endpoints $J(-2,-5)$ and $K(6,-10)$ is $(2,-7.5)$ not $(1,-7)$.