Question

Given square JKLM with J(0, 0), K(4, 0), L(4, 4), and M(0, 4). Show that the diagonals of the square are perpendicular. Explain how you know they are perpendicular.

Answer 1

Answer:

The diagonals of the square JKLM are perpendicular to each other since $\overrightarrow {JL}\,\bullet \,\overrightarrow{KM} = 0$.

Step-by-step explanation:

Let JL and KM the diagonals of the square JKLM, if JL and KM are perpendicular to each other, then $\overrightarrow {JL}\,\bullet \,\overrightarrow{KM} = 0$. First, we determine the value of each vector:

$\overrightarrow{JL} = L(x,y)-J(x,y)$ (1)

$\overrightarrow{JL} = (4,4)-(0,0)$

$\overrightarrow{JL} = (4,4)$

$\overrightarrow{KM} = M(x,y)-K(x,y)$ (2)

$\overrightarrow{KM} = (0,4)-(4,0)$

$\overrightarrow{KM} = (-4,4)$

Then,

$(4, 4)\,\bullet\,(-4,4) = -16+16 = 0$

Therefore, the diagonals of the square JKLM are perpendicular to each other.