Question

The points P(4,3) Q(-5,-1) and T(2,-2) are vertices of a

(a) Equilateral triangle (b) Isosceles triangle (c) Scalene triangle (d) No triangle
please give me right anawer​

Answer 1

Given:

The points

P(4,3)

Q(-5,-1)

T(2,-2)

To find:

The given points are vertices of which type of triangle?

• About types of triangle:

1. Equilateral Triangle - The triangle whose all three sides are equal. The three interior angles of a triangle is 60° each.
2. Isosceles Triangle - The triangle in which only two sides are equal.
3. Scalene triangle - The triangle in which all three sides are different.

Now,

• Finding the distance between the points,

(PQ)² = (-5-4)² + (-1-3)²

         = (-9)² + (-4)²

         = 81 + 16

         = 97

PQ = $\sqrt{97}$ units

Now,

(QT)² = (2+5)² + (-2+1)²

         = (7)² + (-1)²

         = 49 + 1

         = 50

QT = $\sqrt{50}$ units

And,

(PT)² = (2-4)² + (-2-3)²

         = (-2)² + (-5)²

         = 4 + 25

         = 29

PT = $\sqrt{29}$ units

So,

We can conclude that all side are different

PQ ≠ QT ≠ PT

Hence,

It is a Scalene triangle

Option c) Scalene triangle is correct

Answer 2

Answer:

(c) Scalene triangle

Step-by-step explanation:

To find the type of triangle we need to find the length of the side.

So,

By using distance formula we can find the distance of the points.

Distance formula is

If A(x₁ , y₁) and B(x₂ , y₂)

AB² = (x₂ - x₁)² + (y₂ - y₁)²

Now,

(PQ)² = (-5-4)² + (-1-3)²

        = (-9)² + (-4)²

        = 81 + 16

        = 97

PQ =  √97 units

(QT)² = (2+5)² + (-2+1)²

        = (7)² + (-1)²

        = 49 + 1

        = 50

QT = √50 units

(PT)² = (2-4)² + (-2-3)²

        = (-2)² + (-5)²

        = 4 + 25

        = 29

PT =  √29 units

So,

The three sides are different.

So, the type of triangle in which all side are not equal is Scalene triangle.