Question

HELP ASAP! GIVING BRAINLIEST!!


∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side BC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side AC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units.
∠ABC ≈ °
A) 55.21
B) 85.16
C) 105.26
D) 114.11

Answer 1

Answer:

AB is A

BC is B

AC is D

Step-by-step explanation:

To find the length of each side, use the formula for the distance between coordinate pairs.

We can find the distance using the distance formula:

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

AB

We then substitute (-3,6) as $(x_1,y_1)$ and (2,1) as $(x_2,y_2)$.

$d=\sqrt{(2--3)^2+(1-6)^2} \\d=\sqrt{(2+3)^2+(-5)^2} \\d=\sqrt{25+25}\\d=\sqrt{50}$

BC

We then substitute (2,1) as $(x_1,y_1)$ and (9,5) as $(x_2,y_2)$.

$d=\sqrt{(9-2)^2+(5-1)^2} \\d=\sqrt{(-7)^2+(4)^2} \\d=\sqrt{49+16}\\d=\sqrt{65}$

AC

We then substitute (-3,6) as $(x_1,y_1)$ and (9,5) as $(x_2,y_2)$.

$d=\sqrt{(9--3)^2+(5-6)^2} \\d=\sqrt{(12)^2+(-1)^2} \\d=\sqrt{144+1}\\d=\sqrt{145}$