Question

find the distance between the points (5, -4) and (5, 3).

Explanation:

Step1: Identify the formula

Use the distance formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) in a plane: \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1 = 5,y_1=-4,x_2 = 5,y_2 = 3\).

Step2: Substitute the values

Substitute into the formula: \(d=\sqrt{(5 - 5)^2+(3-(-4))^2}\).
First, calculate \((5 - 5)^2=0\) and \((3 + 4)^2=49\).
Then \(d=\sqrt{0 + 49}\).

Step3: Simplify the expression

Since \(\sqrt{49}=7\).

Answer:

\(7\)