Question

what is the the distance between p(-4,3) and q(6,1)? round to the nearest tenth.
a 10.2
b 4.5
c 9.8
d 3.5

Explanation:

Step1: Recall the 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, \( x_1=-4,y_1 = 3,x_2 = 6,y_2=1 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=6-(-4)=6 + 4 = 10 \) and \( y_2 - y_1=1 - 3=-2 \).
Then, \( d=\sqrt{(10)^2+(-2)^2}=\sqrt{100 + 4}=\sqrt{104} \).

Step3: Calculate the square root and round

\( \sqrt{104}\approx10.2 \) (rounded to the nearest tenth).

Answer:

A. 10.2