Question

question 13
find the distance between the points (9, 6) and (24, 38).
○ 12
○ 25.5
○ 35.33
○ 15

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, \( x_1 = 9 \), \( y_1 = 6 \), \( x_2 = 24 \), \( y_2 = 38 \).

Step3: Calculate the differences

First, find \( x_2 - x_1=24 - 9 = 15 \) and \( y_2 - y_1=38 - 6 = 32 \).

Step4: Square the differences

Square these results: \( 15^2 = 225 \) and \( 32^2 = 1024 \).

Step5: Sum the squares

Add them together: \( 225+1024 = 1249 \).

Step6: Take the square root

Now, take the square root of 1249: \( d=\sqrt{1249}\approx35.33 \).

Answer:

35.33