Question

what is the distance between the points (-6, -5) and (10, 25) in the coordinate plane?
a. 16
b. 34
c. 51
d. 30

Explanation:

Step1: Use 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 \(x_1=-6,y_1 = - 5,x_2=10,y_2 = 25\).

Step2: Calculate \(x_2 - x_1\) and \(y_2 - y_1\)

\(x_2 - x_1=10-(-6)=10 + 6=16\), \(y_2 - y_1=25-(-5)=25 + 5=30\).

Step3: Substitute into the formula

\(d=\sqrt{16^{2}+30^{2}}=\sqrt{256 + 900}=\sqrt{1156}\).

Step4: Simplify the square - root

Since \(34\times34 = 1156\), \(\sqrt{1156}=34\).

Answer:

B. 34