Question

Check whether (5, −2), (6, 4) and (7, −2) are the vertices of an isosceles triangle.

Answer 1

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Answer 2

Answer:

Proved that the triangle is an isosceles triangle.

Step-by-step explanation:

In an isosceles triangle, any two of the three sides are of equal length and the third side is different in length.

Given the vertices of a triangle( ΔABC say) are A(5,-2), B(6,4) and C(7,-2).

ΔABC is an isosceles triangle that we have to prove.

Now,  length AB=$\sqrt{(5-6)^{2}+(-2-4)^{2}  } =\sqrt{37}$ units

Length BC= $\sqrt{(6-7)^{2}+(4-(-2))^{2}  } =\sqrt{37}$ units

Again length CA =$\sqrt{(7-5)^{2}+(-2-(-2))^{2}  } =2$ units

Hence, AB= BC≠CA.

Therefore, this triangle is an isosceles triangle. (Proved)