Question

topic: distance & midpoint formula distance formula: 16. given the graph below, find mn.

Explanation:

Step1: Identify coordinates

Assume \(M(x_1,y_1)\) and \(T(x_2,y_2)\) from the graph. Let's say \(M(- 3,-2)\) and \(T(0,3)\).

Step2: Apply distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Substitute \(x_1=-3,y_1 = - 2,x_2 = 0,y_2=3\) into it. First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\): \(x_2 - x_1=0-(-3)=3\) and \(y_2 - y_1=3 - (-2)=5\). Then \((x_2 - x_1)^2+(y_2 - y_1)^2=3^2 + 5^2=9 + 25=34\). So \(d=\sqrt{34}\).

Answer:

\(\sqrt{34}\)