Question

find the distance between the points (5, 9) and (20, 17).
○ 27
○ 11
○ 15
○ 17

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, \( x_1 = 5 \), \( y_1 = 9 \), \( x_2 = 20 \), \( y_2 = 17 \).

Step2: Calculate the differences

First, find \( x_2 - x_1 = 20 - 5 = 15 \) and \( y_2 - y_1 = 17 - 9 = 8 \).

Step3: Substitute into the formula

Substitute these values into the distance formula: \( d=\sqrt{(15)^2+(8)^2}=\sqrt{225 + 64}=\sqrt{289} \).

Step4: Simplify the square root

Since \( \sqrt{289}=17 \), the distance between the two points is 17.

Answer:

D. 17