Question

on the coordinate grid below, point m is halfway between point j and point l (not shown) on a vertical line. which coordinates represent the location of point l (not shown)? (4,6) (4,-9) (4,-1.5) (4,-6.5)

Explanation:

Step1: Recall mid - point formula for vertical line

For two points $(x_1,y_1)$ and $(x_2,y_2)$ on a vertical line ($x_1 = x_2$), the mid - point formula for the y - coordinate is $y_m=\frac{y_1 + y_2}{2}$, where $y_m$ is the y - coordinate of the mid - point. Here $x$ coordinates of $J$, $M$ and $L$ are the same ($x = 4$). Let the coordinates of $J=(4,1)$, $M=(4, - 4)$ and $L=(4,y)$.

Step2: Apply mid - point formula

We know that $y_M=\frac{y_J + y_L}{2}$. Substitute $y_J = 1$ and $y_M=-4$ into the formula: $-4=\frac{1 + y_L}{2}$.

Step3: Solve for $y_L$

Multiply both sides of the equation $-4=\frac{1 + y_L}{2}$ by 2: $-4\times2=1 + y_L$. So, $-8 = 1+y_L$. Then subtract 1 from both sides: $y_L=-8 - 1=-9$.

Answer:

$(4,-9)$