Question

follow these steps to prove the given quadrilateral is a parallelogram.
√ 1. determine the slope of ab: 4/3
√ 2. determine the slope of dc: 4/3

1. determine the length of ab: 5 16 25

Explanation:

Step1: Identify coordinates of A and B

Let's assume \(A(x_1,y_1)\) and \(B(x_2,y_2)\). From the graph, if we count the grid - squares, moving from \(A\) to \(B\), the horizontal change (\(\Delta x=x_2 - x_1\)) and vertical change (\(\Delta y=y_2 - y_1\)) can be used in the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Moving from \(A\) to \(B\), the horizontal displacement is \(3\) units and the vertical displacement is \(4\) units.

Step2: Apply the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(\Delta x = 3\) and \(\Delta y=4\), so \(d=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\).

Answer:

5