Question

find the distance between the points (3, -4) and (-7, -4).

Explanation:

Step1: Identify the formula for distance

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, \(x_1 = 3,y_1=-4,x_2=-7,y_2 = -4\).

Step2: Substitute the values into the formula

Substitute the values: \(d=\sqrt{(-7 - 3)^2+(-4+4)^2}\).
First, calculate \((-7 - 3)^2=(-10)^2 = 100\) and \((-4 + 4)^2=0^2=0\).
Then \(d=\sqrt{100+0}\).

Step3: Simplify the expression

Since \(\sqrt{100+0}=\sqrt{100}\), and \(\sqrt{100}=10\).

Answer:

\(10\)