Question

the distance between two of the points shown is approximately 3.6 units. what are the two points? a a and b b b and c c b and d d c and d

Explanation:

Step1: Find coordinates of points

From the graph, \(A=(0,0)\), \(B=(2,3)\), \(C=(4,5)\), \(D=(5,0)\).

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

• For \(A\) and \(B\): \(d_{AB}=\sqrt{(2 - 0)^2+(3 - 0)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.6\)
• For \(B\) and \(C\): \(d_{BC}=\sqrt{(4 - 2)^2+(5 - 3)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.8\)
• For \(B\) and \(D\): \(d_{BD}=\sqrt{(5 - 2)^2+(0 - 3)^2}=\sqrt{9 + 9}=\sqrt{18}\approx4.2\)
• For \(C\) and \(D\): \(d_{CD}=\sqrt{(5 - 4)^2+(0 - 5)^2}=\sqrt{1 + 25}=\sqrt{26}\approx5.1\)

Answer:

A. \(A\) and \(B\)