Question

The coordinates of the vertices of the triangle are located as follows: upper A at left parenthesis negative 5 comma 2 right parenthesis, upper B at left parenthesis negative 3 comma 5 right parenthesis, and upper C at left parenthesis negative 2 comma negative 1 right parenthesis.


Use a coordinate proof to show that triangle ABC
𝐴
𝐵
𝐶
is scalene. What are the lengths of sides AB
𝐴
𝐵
, BC
𝐵
𝐶
, and AC
𝐴
𝐶
?

(1 point)
Responses

AB≈3.6
𝐴
𝐵
≈
3.6
, BC≈6.1
𝐵
𝐶
≈
6.1
, and AC≈4.2
𝐴
𝐶
≈
4.2
; therefore, ABC
𝐴
𝐵
𝐶
is a scalene triangle.
cap A cap b almost equal to 3 point 6 , cap b cap c almost equal to 6 point 1 , and cap A cap c almost equal to 4 point 2 ; therefore, upper A upper B upper C is a scalene triangle.

AB≈8.5
𝐴
𝐵
≈
8.5
, BC≈6.4
𝐵
𝐶
≈
6.4
, and AC≈7.1
𝐴
𝐶
≈
7.1
; therefore, ABC
𝐴
𝐵
𝐶
is a scalene triangle.
cap A cap b almost equal to 8 point 5 , cap b cap c almo

Answer 1

Use the distance formula: d = sqrt((x2−x1)^2 + (y2−y1)^2).

AB: A(−5,2) to B(−3,5)
- Δx = 2, Δy = 3 ⇒ AB^2 = 2^2 + 3^2 = 13
- AB = √13 ≈ 3.606

BC: B(−3,5) to C(−2,−1)
- Δx = 1, Δy = −6 ⇒ BC^2 = 1^2 + (−6)^2 = 37
- BC = √37 ≈ 6.083

AC: A(−5,2) to C(−2,−1)
- Δx = 3, Δy = −3 ⇒ AC^2 = 3^2 + (−3)^2 = 18
- AC = √18 = 3√2 ≈ 4.243

Since AB^2 = 13, BC^2 = 37, and AC^2 = 18 are all different (so AB, BC, AC are all different), triangle ABC is scalene.