Question

1. the points $(-6,3)$ and $(-3,-7)$ are shown on the coordinate grid. what is the distance, in units, between the two points? a. 109 b. 156 c. $sqrt{109}$ d. $sqrt{156}$

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-6,3)\) and \((x_2,y_2)=(-3,-7)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(x_2 - x_1=-3-(-6)=3\), \(y_2 - y_1=-7 - 3=-10\)

Step3: Calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\)

\((3)^2+(-10)^2=9 + 100=109\)

Step4: Find the square root

\(d=\sqrt{109}\)

Answer:

C. \(\sqrt{109}\)