Question

for the point ( p(-25,16) ) and ( q(-18,19) ), find the distance ( d(p,q) ) and the coordinates of the midpoint ( m ) of the segment ( pq ). what is the distance? (simplify your answer. type an exact answer, using radicals as need.)

Explanation:

Step1: Use the distance formula

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 \(x_1=-25,y_1 = 16,x_2=-18,y_2 = 19\).

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Step2: Simplify the expression inside the square - root

First, calculate \((-18 + 25)=7\) and \((19 - 16)=3\). Then \(d=\sqrt{7^2+3^2}\).
Since \(7^2 = 49\) and \(3^2=9\), we have \(d=\sqrt{49 + 9}\).

Step3: Calculate the final value

\(49+9=58\), so \(d=\sqrt{58}\).

Answer:

\(\sqrt{58}\)