Question

what is the distance between points a(-3,2) and b(5,-4)?

Explanation:

Step1: Identify the coordinates

Let \(A(x_1,y_1)=(-3,2)\) and \(B(x_2,y_2)=(5,-4)\).

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(x_2 - x_1=5-(-3)=8\), \(y_2 - y_1=-4 - 2=-6\).
Then \(d=\sqrt{8^2+(-6)^2}=\sqrt{64 + 36}=\sqrt{100}\).

Step3: Simplify the square - root

\(\sqrt{100}=10\).

Answer:

10 units