Question

find the distance between the points (4,6) and (4, - 7).

Explanation:

Step1: Identify the formula

For two points \((x_1,y_1)\) and \((x_2,y_2)\), the distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1 = 4,y_1=6,x_2 = 4,y_2=-7\).

Step2: Substitute the values

Substitute into the formula: \(d=\sqrt{(4 - 4)^2+(-7 - 6)^2}\).
First, calculate \((4 - 4)^2=0\) and \((-7 - 6)^2=(-13)^2 = 169\).
So \(d=\sqrt{0 + 169}\).

Step3: Simplify the expression

Since \(\sqrt{0+169}=\sqrt{169}\), and \(\sqrt{169}=13\).

Answer:

\(13\)