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

Step2: Substitute values into mid - point formula

We know that $y_m=-4$, $y_1 = 1$ and we want to find $y_2$. Using the formula $y_m=\frac{y_1 + y_2}{2}$, we substitute: $-4=\frac{1 + y}{2}$.

Step3: Solve the equation for $y$

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

Answer:

$(4,-9)$