Question

1. what is the distance between the points m(-8,11) and n(3,7)?

18.7
10.2
11.7
19.4

Explanation:

Step1: Identify the coordinates

Given \(M(-8,11)\) and \(N(3,7)\), so \(x_1=-8,y_1 = 11,x_2=3,y_2=7\)

Step2: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(3-(-8))^2+(7 - 11)^2}=\sqrt{(3 + 8)^2+(-4)^2}=\sqrt{11^2+(-4)^2}\)

Step3: Calculate the squares

\(11^2 = 121\) and \((-4)^2=16\), so \(d=\sqrt{121 + 16}=\sqrt{137}\)

Step4: Find the square - root

\(\sqrt{137}\approx11.7\)

Answer:

\(11.7\)