Answer:
The area of the rectangle VWXY is 52 square units
Explanation:
The formula of the area of the rectangle is A = L × W, where
- L is the length of the rectangle
- W is the width of the rectangle
- If a line segment has endpoints (x1, y) and (x2, y), then the line segment is horizontal and its length = x2 - x1
- If a line segment has endpoints (x, y1) and (x, y2), then the line segment is vertical and its length = y2 - y1
From the given figure
∵ VWXY is a rectangle
∵ V = (3, -9) and W = (-1, -9)
∵ X = (-1, 4) and Y = (3, 4)
∵ Its length is WX or VY
∴ WX = VY
∵ Its width is VW or XY
∴ VW = XY
→ Let us find its length and its width
∵ Points W and X have the same x-coordinates
∴ y1 = -9 and y2 = 4
→ By using the 4th note above
∴ WX = 4 - -9 = 4 + 9 = 13
∴ L = 13 units
∵ Points X and Y have the same y-coordinates
∴ x1 = -1 and x2 = 3
→ By using the 3rd note above
∴ XY = 3 - -1 = 3 + 1 = 4
∴ W = 4 units
→ By using the formula of the area above
∵ A = 13 × 4
∴ A = 52 square units
∴ The area of the rectangle VWXY is 52 square units