Answered: "Check whether (5,-2), (6,4) and (7,-2) are the..."

Skylar Greer

Answered question

2023-01-20

Check whether

(5, - 2)

(6, 4)

and

(7, - 2)

are the vertices of an isosceles triangle.

Answer & Explanation

hachatpg9

Beginner2023-01-21Added 14 answers

Let

A (5, - 2), B (6, 4)

and

C (7, - 2)

are the vertices of a triangle.
We will calculate the distances between each point to see if they are all vertices of an isosceles triangle.
Distance formula

= {(x 2 - x 1)}^{2} + {(y 2 - y 1)}^{2}

finding the separation between two points

A (5, - 2)

and

B (6, 4)

, let

x 1 = 5, y 1 = - 2

and

x 2 = 6, y 2 = 4

AB = {(x 2 - x 1)}^{2} + {(y 2 - y 1)}^{2} = {(6 - 5)}^{2} + {(4 - (- 2))}^{2} = 1^{2} + 6^{2} = 37 unit

To find the distance between points

B (6, 4)

and

C (7, - 2)

, let

x 1 = 6, y 1 = 4

and

x 2 = 7, y 2 = - 2

BC = {(x 2 - x 1)}^{2} + {(y 2 - y 1)}^{2} = {(7 - 6)}^{2} + {(- 2 - (4))}^{2} = 1^{2} + {(- 6)}^{2} = 37 unit

To find the distance between points

C (7, - 2)

and

A (5, - 2)

, let

x 1 = 7, y 1 = - 2,

and

x 2 = 5, y 2 = - 2

CA = {(x 2 - x 1)}^{2} + {(y 2 - y 1)}^{2} = {(5 - 7)}^{2} + {(- 2 - (- 2))}^{2} = {(- 2)}^{2} + {(0)}^{2} = 4 = 2 unit

∵

Given that AB and BC have equal lengths, the given points are isosceles triangle's vertices.
Thus,

(5, - 2)

(6, 4)

and

(7, - 2)

are the vertices of an isosceles triangle.

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