Question

If Quadrilateral JKLM is a square, where points J(0, 5), K(4, 7), L(?, ?) and M(2, 1) areknown. Find the coordinates of point L

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given points

$\begin{gathered} J(0,5) \\ K(4,7) \\ L(x,y) \\ M(2,1) \end{gathered}$

STEP 2: Get the points

Using the midpoint formula,

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

For a square, the diagonal(midpoint) must be equal, therefore

$\begin{gathered} Using\text{ midpoint formula,} \\ (\frac{x+0}{2},\frac{y+5}{2})=(\frac{4+2}{2},\frac{7+1}{2}) \\ (\frac{x}{2},\frac{y+5}{2})=(\frac{6}{2},\frac{8}{2}) \\ (\frac{x}{2},(\frac{y+5}{2})=(3,4) \end{gathered}$

Solve for x:

$\begin{gathered} \frac{x}{2}=3 \\ Cross\text{ multiply,} \\ x=3\times2=6 \end{gathered}$

Solve for y:

$\begin{gathered} \frac{y+5}{2}=4 \\ Cross\text{ multiply:} \\ y+5=8 \\ y=8-5 \\ y=3 \end{gathered}$

Hence, the coordinates of L are:

$(6,3)$