Question

question 4
what is the distance between the two endpoints in the graph below? if necessary, round your answer to two decimal places.
a. 10 units
b. 5 units
c. 7.07 units
d. 8.49 units

question 5
what is the distance between the points (22, 27) and (2, -10)? if necessary, round your answer to two decimal places.
a. 31.13 units
b. 37 units
c. 57 units
d. 42.06 units

question 6
what is the perimeter of the rectangle shown below?
a. 13 units
b. 18 units
c. 26 units
d. 40 units

question 7
what is the area of a square with sides of length 6?
a. 18 square units
b. 12 square units
c. 36 square units
d. 24 square units

Explanation:

Question 4

Step1: Recall distance formula

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

Step2: Substitute points $(-3,-2),(2,3)$

$d=\sqrt{(2-(-3))^2+(3-(-2))^2}=\sqrt{(5)^2+(5)^2}$

Step3: Calculate and simplify

$d=\sqrt{25+25}=\sqrt{50}\approx7.07$

Question 5

Step1: Use distance formula

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute points $(22,27),(2,-10)$

$d=\sqrt{(2-22)^2+(-10-27)^2}=\sqrt{(-20)^2+(-37)^2}$

Step3: Calculate and simplify

$d=\sqrt{400+1369}=\sqrt{1769}\approx42.06$

Question 6

Step1: Identify rectangle side lengths

Length $l=5$, width $w=8$

Step2: Use perimeter formula $P=2(l+w)$

$P=2(5+8)$

Step3: Compute the value

$P=2\times13=26$

Question 7

Step1: Use square area formula $A=s^2$

$s=6$, so $A=6^2$

Step2: Calculate the value

$A=36$

Answer:

Question 4: C. 7.07 units
Question 5: D. 42.06 units
Question 6: C. 26 units
Question 7: C. 36 square units