Question

for all of the problems on this quiz, you must show evidence of your thinking. sc 4: i can apply the pythagorean theorem and its cousin, the distance formula 1a) a basketball hoop rim should be exactly 10 feet above the court. does this basketball hoop need to be raised or lowered? if so, by how much? 1b) point a is (-3, 15); point b is (12, 51). how long is line segment ab?

Explanation:

Step1: Analyze height of basketball hoop

The standard height is 10 ft and the current height is 10.1 ft.

Step2: Calculate height adjustment

Subtract the standard height from the current height: $10.1 - 10=0.1$ ft. Since the result is positive, the hoop needs to be lowered.

Step3: Calculate length of line - segment AB

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-3,y_1 = 15,x_2=12,y_2 = 51$.
First, calculate $(x_2 - x_1)$ and $(y_2 - y_1)$:
$x_2 - x_1=12-(-3)=15$
$y_2 - y_1=51 - 15 = 36$
Then, calculate $(x_2 - x_1)^2+(y_2 - y_1)^2$:
$(x_2 - x_1)^2+(y_2 - y_1)^2=15^2+36^2=225 + 1296=1521$
Finally, find the square - root:
$d=\sqrt{1521}=39$

Answer:

1a) The basketball hoop needs to be lowered by 0.1 ft.
1b) The length of line segment AB is 39.