Question

find the distance between the points.
(4,5) and (-2,5)

the distance is \\(\square\\).

Explanation:

Step1: Recall the distance formula for two points \((x_1,y_1)\) and \((x_2,y_2)\)

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For the points \((4,5)\) and \((-2,5)\), we have \(x_1 = 4\), \(y_1 = 5\), \(x_2=-2\), \(y_2 = 5\).

Step2: Substitute the values into the formula

First, calculate the differences in \(x\) and \(y\) coordinates. The difference in \(x\) - coordinates: \(x_2 - x_1=-2 - 4=-6\). The difference in \(y\) - coordinates: \(y_2 - y_1=5 - 5 = 0\).
Then, substitute these into the distance formula: \(d=\sqrt{(-6)^2+0^2}\).

Step3: Simplify the expression

Calculate \((-6)^2 = 36\) and \(0^2 = 0\). So \(d=\sqrt{36 + 0}=\sqrt{36}\). Since \(\sqrt{36}=6\), the distance is 6.

Answer:

6