Question

find the magnitude of (overrightarrow{ij}) with (i(-9,4)) and (j(-9,9)). write your answer in simplified form.

Explanation:

Step1: Recall the distance formula

The magnitude of a vector \(\overrightarrow{IJ}\) with \(I(x_1,y_1)\) and \(J(x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1=-9,y_1 = 4,x_2=-9,y_2=9\).

Step2: Substitute the values into the formula

Substitute the values: \((x_2 - x_1)=-9-(-9)=0\) and \((y_2 - y_1)=9 - 4=5\). Then \(d=\sqrt{(0)^2+(5)^2}\).

Step3: Simplify the expression

Since \((0)^2+(5)^2=0 + 25=25\), then \(d=\sqrt{25}\).

Answer:

\(5\)