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∆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

1. Option A

2. Option B

3. Option D

4. Option C

Step-by-step explanation:

The given vertices of triangle ABC are A(-3, 6), B(2,1), C(9, 5).

We have to fine the distance AB, BC and AC.

To calculate the distance between two vertices we will use the formula

For the length of side AB

AB=

Option A. is the correct option

For the length of side BC

Option B is the answer.

For the length of side AC

Option D is the answer.

For ∠ABC we will use the formula

Since angle ABC is formed by two sides AB and BC

So we will find the slopes of these two lines and find the angle

Now slope of AB,

Slope of BC,

Since angle between them is negative that means angle theta will be obtuse angle.

So the angle between AB and BC = (180 - 74.75) = 105.26°

Therefore Option C. 105.26° is the answer.