Question

Calculate the area of triangle WXY with altitude YZ, given W(2, −1), X(6, 3), Y(7, 0), and Z(5, 2). (6 points) 8 square units 9.4 square units 7.7 square units 12 square units

Answer 1

Answer: 8 square units

Step-by-step explanation:

Answer 2

The area of triangle WXY with altitude YZ is: 8 square units.

Area of a Triangle

Area = 1/2(base × height)

Altitude = height.

Given:

Base = WX = distance between W(2, −1) and X(6, 3):

Using distance formula, $WX = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$:

$WX = \sqrt{(3 - (-1))^2 + (6 - 2)^2}\\\\\mathbf{WX = 5.7 units}$

Altitude/height = YZ = distance between Y(7, 0), and Z(5, 2):

$YZ = \sqrt{(0 - 2)^2 + (7 - 5)^2}\\\\\mathbf{YZ = 2.8 units}$

Area of triangle WXY = 1/2(WX × YZ)

Area of triangle WXY = 1/2(5.7 × 2.8) = 7.98

Area = 8 square units.

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