Question

show what you know
what is the distance between the points $(-3, -2)$ and $(4, 5)$?
7.0 units
5.5 units
10.5 units
9.9 units

Explanation:

Step1: Recall 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, \(x_1=-3,y_1 = - 2,x_2=4,y_2=5\).

Step2: Substitute the values into the formula

First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
\(x_2 - x_1=4-(-3)=4 + 3=7\)
\(y_2 - y_1=5-(-2)=5 + 2=7\)
Then, \((x_2 - x_1)^2+(y_2 - y_1)^2=7^2+7^2=49 + 49=98\)

Step3: Calculate the square - root

\(d=\sqrt{98}\approx9.9\) (since \(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\approx7\times1.414 = 9.898\approx9.9\))

Answer:

9.9 units