Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

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

Answer :

Let A = (5, –2), B = (6, 4) and C = (7, –2)
Using Distance Formula to find distances AB, BC and CA.

AB = $$\sqrt{(6-5)^2 + (4 + 2)^2}$$
$$= \sqrt{1^2 - 6^2}$$
$$= \sqrt{1 + 36}$$
$$= \sqrt{37}$$

BC = $$\sqrt{(7-6)^2 + (-2 - 4)^2}$$
$$= \sqrt{1^2 - (-6)^2}$$
$$= \sqrt{1 + 36}$$
$$= \sqrt{37}$$

CA = $$\sqrt{(7-5)^2 + (-2 + 2)^2}$$
$$= \sqrt{2^2 - 0}$$
$$= \sqrt{4}$$
$$= 2$$
Since AB = BC.

Therefore, A, B and C are vertices of an isosceles triangle.