Question

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

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

Step2: Substitute the values

Substitute into the formula: \(d=\sqrt{(-3-(-3))^2+(4 - 7)^2}\).
Simplify the \(x\) - terms: \(-3-(-3)=-3 + 3=0\).
Simplify the \(y\) - terms: \(4-7=-3\).
So \(d=\sqrt{0^2+(-3)^2}\).

Step3: Calculate the distance

Since \(0^2 = 0\) and \((-3)^2=9\), then \(d=\sqrt{0 + 9}=\sqrt{9}\).
And \(\sqrt{9}=3\).

Answer:

\(3\)