Question

unit 7
coordinate geometry
lesson 8
coordinate geometry unit test
back to intro page
to the nearest tenth of a unit, what is the distance between points a and b?

Explanation:

Step1: Determine the coordinates of points A and B

From the graph, point \(A\) has coordinates \((-3,5)\) and point \(B\) has coordinates \((7,2)\).

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

Let \((x_1,y_1)=(-3,5)\) and \((x_2,y_2)=(7,2)\).
First, calculate \((x_2 - x_1)\): \(7-(-3)=7 + 3=10\)
Then, calculate \((y_2 - y_1)\): \(2 - 5=-3\)
Substitute into the formula: \(d=\sqrt{(10)^2+(-3)^2}=\sqrt{100 + 9}=\sqrt{109}\)

Step3: Calculate the numerical value

\(\sqrt{109}\approx10.4\)

Answer:

\(10.4\)