Question

Verify that parallelogram WXYZ with vertices W(-10, -2), X(-18,12), Y(-2,10), and Z (6,-4) is a rhombus by showing that it is a parallelogram with perpendicular diagonals.

Answer 1

The parallelogram WXYZ is a rhombus because its diagonals are perpendicular

Step-by-step explanation:

The product of the slopes of two perpendicular lines is -1, that

means if the slope of one of them is m, then the slope of the

other is $\frac{-1}{m}$

• The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
• $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points on the line

∵ WXYZ is a parallelogram

∵ W (-10 , -2) , X (-18 , -12) , Y (-2 , 10) , Z (6 , -4)

∵ Its diagonals are WY and XZ

- Find the slope of WY

∵ W = (-10 , -2) and Y = (-2 , 10)

∴ $x_{1}$ = -10 and $x_{2}$ = -2

∴ $y_{1}$ = -2 and $y_{2}$ = 10

∴ $m_{WY}=\frac{10--2}{-2--10}=\frac{12}{8}$

- Divide up and down by 4 to reduce it to its simplest form

∴ $m_{WY}=\frac{3}{2}$

- Find the slope of XZ

∵ X = (-18 , 12) and Z = (6 , -4)

∴ $x_{1}$ = -18 and $x_{2}$ = 6

∴ $y_{1}$ = 12 and $y_{2}$ = -4

∴ $m_{XZ}=\frac{-4-12}{6--18}=\frac{-16}{24}$

- Divide up and down by 8 to reduce it to its simplest form

∴ $m_{XZ}=\frac{-2}{3}$

∵ $(m_{WY}).(m_{XZ})=(\frac{3}{2})(\frac{-2}{3})=\frac{-6}{6}=-1$

∴ WY ⊥ XZ

∴ The diagonals of the parallelogram are perpendicular

∴ The parallelogram WXYZ is a rhombus

The parallelogram WXYZ is a rhombus because its diagonals are perpendicular

Learn more:

You can learn more about parallelograms in brainly.com/question/4459688

#LearnwithBrainly