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

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,

`((x_1+x_2)/(2),(y_1+y_2)/(2))`

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

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

Solve for x:

`\begin{gathered} (x)/(2)=3 \\ Cross\text{ multiply,} \\ x=3*2=6 \end{gathered}`

Solve for y:

`\begin{gathered} (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)`