What is the area of a rectangle with vertices at (1, 1), (1, 5), (4, 1), and (4,

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Question: What is the area of a rectangle with vertices at (1, 1), (1, 5), (4, 1), and (4, 5)? (2021)

Options:

Correct Answer: 12

Exam Year: 2021

Solution:

Area = length * width = (4-1) * (5-1) = 3 * 4 = 12.

What is the area of a rectangle with vertices at (1, 1), (1, 5), (4, 1), and (4, 5)? (2021)

What is the area of a rectangle with vertices at (1, 1), (1, 5), (4, 1), and (4, 5)? (2021)

Step 1: Identify the coordinates of the rectangle's vertices: (1, 1), (1, 5), (4, 1), and (4, 5).
Step 2: Determine the length of the rectangle. The length is the distance between the x-coordinates of the vertices (4 and 1). Calculate it: 4 - 1 = 3.
Step 3: Determine the width of the rectangle. The width is the distance between the y-coordinates of the vertices (5 and 1). Calculate it: 5 - 1 = 4.
Step 4: Calculate the area of the rectangle using the formula: Area = length * width.
Step 5: Substitute the values into the formula: Area = 3 * 4.
Step 6: Perform the multiplication: 3 * 4 = 12.
Step 7: Conclude that the area of the rectangle is 12.

Coordinate Geometry – Understanding how to determine the dimensions of a rectangle using the coordinates of its vertices.
Area Calculation – Applying the formula for the area of a rectangle, which is length multiplied by width.