Question

what is the approximate distance between points p and q? round your answer to the nearest hundredths.
a. 4 units
b. 4.12 units
c. 4.89 units
d. 5.1 units

Explanation:

Step1: Identify coordinates

Let \(P(-3, - 4)\) and \(Q(2,-3)\).

Step2: Apply distance formula

The distance \(d\) 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 \(x_1=-3,y_1 = - 4,x_2=2,y_2=-3\). So \(d=\sqrt{(2-(-3))^2+((-3)-(-4))^2}=\sqrt{(2 + 3)^2+(-3 + 4)^2}=\sqrt{5^2+1^2}=\sqrt{25 + 1}=\sqrt{26}\).

Step3: Calculate the value

\(\sqrt{26}\approx5.10\) (rounded to the nearest hundredth).

Answer:

D. 5.10 units