Question

1. calculate the distance between points d and f if d (-4, 9) and f (5, 4). give the exact distance as a radical.

distance: ________________________

Explanation:

Step1: Identify the coordinates

Let \( (x_1,y_1)=(-4,9) \) and \( (x_2,y_2)=(5,4) \).

Step2: Use the distance formula

The distance formula is \( d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Substitute the values: \( x_2 - x_1=5-(-4)=5 + 4=9 \), \( y_2 - y_1=4 - 9=-5 \).
Then \( d=\sqrt{9^2+(-5)^2} \).

Step3: Calculate the squares

\( 9^2 = 81 \), \( (-5)^2=25 \).
So \( d=\sqrt{81 + 25} \).

Step4: Sum and simplify

\( 81+25 = 106 \).

Answer:

\(\sqrt{106}\)