Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-4, 2) and (3, 5) answer

Explanation:

Step1: Recall distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-4,y_1 = 2,x_2=3,y_2 = 5\).

Step2: Substitute values into formula

First, calculate \(x_2 - x_1=3-(-4)=3 + 4=7\) and \(y_2 - y_1=5 - 2 = 3\). Then, substitute into the formula: \(d=\sqrt{(7)^2+(3)^2}=\sqrt{49 + 9}=\sqrt{58}\).

Step3: Calculate and round

\(\sqrt{58}\approx7.6\) (since \(\sqrt{58}\approx7.61577\) and rounding to the nearest tenth gives \(7.6\)).

Answer:

\(7.6\)