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icang [17]
3 years ago
6

Triangle ABC has vertices at A(−1 , 2), B(4, 2), and C(3, −1). Classify the triangle according to the side lengths.

Mathematics
2 answers:
Orlov [11]3 years ago
6 0

Answer:

B) Isosceles

Step-by-step explanation:

The given triangle has vertices at A(-1,2), B(4,2) and C(3,-1).

We must first determine the length of the sides of the triangle, before we can classify it.

We apply the distance formula to find length of the sides.

|AB|=\sqrt{(4--1)^2+(2-2)^2}

\Rightarrow |AB|=\sqrt{(4+1)^2+(2-2)^2}

\Rightarrow |AB|=\sqrt{5^2+(0)^2}

\Rightarrow |AB|=\sqrt{25}

\Rightarrow |AB|=5 units.

The length of side BC

|BC|=\sqrt{(3-4)^2+(-1-2)^2}

\Rightarrow |BC|=\sqrt{(-1)^2+(-3)^2}

\Rightarrow |BC|=\sqrt{1+9}

\Rightarrow |BC|=\sqrt{10}

The length of side AC

|AC|=\sqrt{(3--1)^2+(-1-2)^2}

We simplify to obtain;

|AC|=\sqrt{(3+1)^2+(-3)^2}

\Rightarrow |AC|=\sqrt{(4)^2+(-3)^2}

|AC|=\sqrt{16+9}

|AC|=\sqrt{25}

|AC|=5\:units

Since |AC|=5\:units=|AB|, the given triangle is an isosceles triangle.

The correct answer is

Pachacha [2.7K]3 years ago
4 0

Answer:

B) isosceles

Step-by-step explanation:

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