Question

find the distance between the pair of points (7,-2) and (5,-6)

Explanation:

Step1: Identify the formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Substitute the values

Here \(x_1=-7,y_1 = - 2,x_2 = 5,y_2=-6\).
Substitute into the formula: \(d=\sqrt{(5-(-7))^2+(-6 - (-2))^2}\).
Simplify inside the square - root: \((5 + 7)^2+( - 6+2)^2\).
\(d=\sqrt{(12)^2+(-4)^2}\).

Step3: Calculate the squares

\((12)^2 = 144\) and \((-4)^2=16\).
So \(d=\sqrt{144 + 16}\).
\(d=\sqrt{160}\).

Step4: Simplify the square - root

\(\sqrt{160}=\sqrt{16\times10}=4\sqrt{10}\approx4\times3.162 = 12.648\).

Answer:

The distance between the points \((-7,-2)\) and \((5,-6)\) is \(4\sqrt{10}\approx12.65\).