Question

for each of the following, find the distance between the points. 18. (3, 8), (9, 10) 19. (6, 4), (-5, -1) 20. (-5, 6), (8, -4) 21. (-6, -4) 22. 23. for each of the following, find the perimeter of the shape. 24. 25. 26. point a is located at (2,2) and the length of the segment is 10 units. which of the following could be the other endpoint? a. (7, 3) b. (-6, -4) c. (5, 0) d. (-3, -1)

Explanation:

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: Calculate distance for point A and option a

For point $A(2,2)$ and $(7,3)$:
$d=\sqrt{(7 - 2)^2+(3 - 2)^2}=\sqrt{5^2+1^2}=\sqrt{25 + 1}=\sqrt{26}
eq10$.

Step3: Calculate distance for point A and option b

For point $A(2,2)$ and $(-6,-4)$:
$d=\sqrt{(-6 - 2)^2+(-4 - 2)^2}=\sqrt{(-8)^2+(-6)^2}=\sqrt{64+36}=\sqrt{100}=10$.

Step4: Calculate distance for point A and option c

For point $A(2,2)$ and $(5,0)$:
$d=\sqrt{(5 - 2)^2+(0 - 2)^2}=\sqrt{3^2+(-2)^2}=\sqrt{9 + 4}=\sqrt{13}
eq10$.

Step5: Calculate distance for point A and option d

For point $A(2,2)$ and $(-3,-1)$:
$d=\sqrt{(-3 - 2)^2+(-1 - 2)^2}=\sqrt{(-5)^2+(-3)^2}=\sqrt{25 + 9}=\sqrt{34}
eq10$.

Answer:

b. $(-6,-4)$