Question

question 7
when you use the distance formula, you are building a right triangle whose ______ connects the given points.
a. longer leg
b. right angle
c. shorter leg
d. hypotenuse

question 8
if $a = (9, 18)$ and $b = (1, 12)$, what is the length of $overline{ab}$?
a. 12 units
b. 10 units
c. 11 units
d. 9 units

question 9
if $a = (-1, -3)$ and $b = (11, -8)$, what is the length of $overline{ab}$?
a. 13 units
b. 11 units
c. 12 units
d. 14 units

question 10
if $a = (0, 0)$ and $b = (8, 2)$, what is the length of $overline{ab}$?
a. 7.75 units
b. 8.25 units
c. 3.16 units
d. 9.41 units

Explanation:

Question 7:

Step1: Recall distance formula logic

The distance formula is derived from the Pythagorean theorem, where the segment between two points forms the side of the right triangle that connects the two points directly.

Question 8:

Step1: Identify distance formula

The distance formula for points $A=(x_1,y_1)$ and $B=(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute values

$x_1=9,y_1=18,x_2=1,y_2=12$
$d=\sqrt{(1-9)^2+(12-18)^2}=\sqrt{(-8)^2+(-6)^2}$

Step3: Calculate squares and sum

$\sqrt{64+36}=\sqrt{100}$

Step4: Simplify square root

$\sqrt{100}=10$

Question 9:

Step1: Apply distance formula

$A=(-1,-3), B=(11,-8)$
$d=\sqrt{(11-(-1))^2+(-8-(-3))^2}=\sqrt{(12)^2+(-5)^2}$

Step2: Compute squares and sum

$\sqrt{144+25}=\sqrt{169}$

Step3: Simplify square root

$\sqrt{169}=13$

Question 10:

Step1: Use distance formula

$A=(0,0), B=(8,2)$
$d=\sqrt{(8-0)^2+(2-0)^2}=\sqrt{8^2+2^2}$

Step2: Calculate squares and sum

$\sqrt{64+4}=\sqrt{68}$

Step3: Approximate square root

$\sqrt{68}\approx8.25$

Answer:

Question 7: D. hypotenuse
Question 8: B. 10 units
Question 9: A. 13 units
Question 10: B. 8.25 units