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
- The formula of the slope of a line is
- and 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)
∴ = -10 and = -2
∴ = -2 and = 10
∴
- Divide up and down by 4 to reduce it to its simplest form
∴
- Find the slope of XZ
∵ X = (-18 , 12) and Z = (6 , -4)
∴ = -18 and = 6
∴ = 12 and = -4
∴
- Divide up and down by 8 to reduce it to its simplest form
∴
∵
∴ 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
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