PLEASE HELP ME? Will mark brainliest?

Triangle ABC has vertices located at A( 0, 2), B (2, 5), and C (−1, 7).

Part A: Find the length of each side of the triangle. Show your work. (4 points)

Part B: Find the slope of each side of the triangle. Show your work. (3 points)

Part C: Classify the triangle. Explain your reasoning. (3 points)\

Thanks!

Perimeter of the triangle = 12 units.

Step-by-step explanation:

Step 1:

Construct a triangle ABC with the given vertices:

Step 2:

Perimeter of the triangle ABC :

¯¯¯¯¯¯

A

B

+

¯¯¯¯¯¯

B

C

+

¯¯¯¯¯¯

A

C

¯¯¯¯¯¯

A

B

refers to the distance between the two points A and B

.

To find the magnitudes of the sides AB, BC and AC, use the distance formula:

Distance between two points

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

Step 3:

Distance(D) between the two points:

A

(

2

,

0

)

and

B

(

2

,

−

3

)

D

=

¯¯¯¯¯¯

A

B

=

√

(

2

−

2

)

2

+

(

−

3

−

0

)

2

⇒

√

9

⇒

3

Distance between the Points A and B: 3 Units

Step 4:

Distance between two points:

B

(

2

,

−

3

)

and

c

(

−

2

,

−

3

)

D

=

¯¯¯¯¯¯

B

C

=

√

(

−

2

−

2

)

2

+

(

−

3

−

(

−

3

)

2

)

⇒

√

(

−

4

)

2

⇒

√

16

⇒

5

Distance between the Points B and C: 4 Units

Step 5:

Distance between two points:

A

(

2

,

0

)

and

C

(

−

2

,

−

3

)

D

=

¯¯¯¯¯¯

A

C

=

√

(

−

2

−

2

)

2

+

(

−

3

−

0

)

2

⇒

√

(

−

4

)

2

+

(

−

3

)

2

⇒

√

16

+

9

⇒

√

25

⇒

5

Distance between the Points A and C: 5 Units

Step 6:

Hence, the Perimeter of the triangle ABC

=

3

+

4

+

5

=

12

Units

Step 7:

Measure the distances between points on the coordinate plane:

Step 8:

Useful information

Measure the angle

∠

A

B

C

Verify that the angle is

90

∘

Hence, triangle

A

B

C

is a right-triangle.

Hope it helps.