Question

find the distance between the points (-7,3) and (2,3).
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Explanation:

Step1: Identify the formula for distance between two points

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-7,y_1 = 3,x_2=2,y_2 = 3\).

Step2: Substitute the values into the formula

Substitute the values into the formula: \(d=\sqrt{(2-(-7))^2+(3 - 3)^2}\).
Simplify the expressions inside the square - root:

• For the \(x\) - part: \(2-(-7)=2 + 7=9\).
• For the \(y\) - part: \(3-3 = 0\).

So, \(d=\sqrt{9^2+0^2}\).

Step3: Calculate the value

Calculate \(9^2+0^2=81+0 = 81\). Then \(d=\sqrt{81}\).
Since \(\sqrt{81}=9\).

Answer:

\(9\)