Question

1 given the vertices of a rectangle at (1, 2), (1, 6), (5, 2), and (5, 6) on the coordinate plane, what is its area?

Explanation:

Step1: Find the length of the base

The base can be found by calculating the distance between \((1, 2)\) and \((5, 2)\). Since the y - coordinates are the same, we use the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) which is \(d=\vert x_2 - x_1\vert\) (when \(y_1 = y_2\)). So, the length of the base \(b=\vert5 - 1\vert=4\).

Step2: Find the length of the height

The height can be found by calculating the distance between \((1, 2)\) and \((1, 6)\). Since the x - coordinates are the same, we use the formula \(d=\vert y_2 - y_1\vert\) (when \(x_1 = x_2\)). So, the length of the height \(h=\vert6 - 2\vert = 4\).

Step3: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A=b\times h\). Substituting \(b = 4\) and \(h=4\) into the formula, we get \(A = 4\times4=16\).

Answer:

16