Question

calculate the distance between the points $q=(-7,1)$ and $m=(-1,9)$ in the coordinate plane.
give an exact answer (not a decimal approximation).

Explanation:

Step1: Identify the coordinates

Given \( Q(-7,1) \) and \( M(-1,9) \). Here \( x_1=-7,y_1 = 1,x_2=-1,y_2=9 \).

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: \(d=\sqrt{(-1-(-7))^2+(9 - 1)^2}\).
Simplify inside the square - root:
First, \(-1-(-7)=-1 + 7=6\) and \(9 - 1=8\).
So \(d=\sqrt{6^2+8^2}\).
Since \(6^2 = 36\) and \(8^2=64\), then \(d=\sqrt{36 + 64}\).
\(36+64 = 100\), so \(d=\sqrt{100}\).

Answer:

\(10\)