Write the name of a triangle with the vertices (1, -3), (6, 2) and (0,4)?
Scalene triangle
Isosceles triangle
Right -angle triangle
Equilateral triangle
Correct answer is B
Let A = (1, -3), B = (6, 2) and C = (0,4)
\(d =\sqrt{ (y_2 - y_1)^2 + (x_2 - x_1)^2}\)
|AB| = \(\sqrt{(2 - (-3))^2 + (6 - 1)^2}\)
= \(\sqrt{(2 + 3)^2 + (6 - 1)^2}\)
= \(\sqrt{5^2 + 5^2}\)
= \(\sqrt{25 + 25}\)
= \(\sqrt50\)
= 5\(\sqrt2\) units
|BC| = \(\sqrt{(4 - 2)^2 + (0 - 6)^2}\)
= \(\sqrt{2^2 + (-6)^2}\)
= \(\sqrt{4 + 36}\)
= \(\sqrt40\)
= 2\(\sqrt10\) units
|AC| = \(\sqrt{(4 - (-3)^2 + (0 - 1)^2}\)
= \(\sqrt{(4 + 3)^2 + (0 - 1)^2}\)
= \(\sqrt{7^2 + (-1)^2}\)
= \(\sqrt{49 + 1}\)
= \(\sqrt50\)
= 5\(\sqrt{2}\) units
Since two sides are equal (|AB| = |AC|), then the triangle is Isosceles.