Question

question 7 of 10
what is the distance between the points (4, 5) and (10, 13) on a coordinate plane?

a. 12 units
b. 8 units
c. 10 units
d. 14 units

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify the coordinates

Here, \( x_1 = 4 \), \( y_1 = 5 \), \( x_2 = 10 \), and \( y_2 = 13 \).

Step3: Calculate the differences

First, find \( x_2 - x_1 = 10 - 4 = 6 \) and \( y_2 - y_1 = 13 - 5 = 8 \).

Step4: Substitute into the formula

Substitute these values into the distance formula: \( d = \sqrt{6^2 + 8^2} \).

Step5: Simplify the expression

Calculate \( 6^2 = 36 \) and \( 8^2 = 64 \). Then, \( 36 + 64 = 100 \). So, \( d = \sqrt{100} = 10 \).

Answer:

C. 10 units