Discussion
The vertices of a triangle are (0, 6), (-5, 3) and (5, 3). The triangle is:
Answer: D
Correct answer: Isosceles
Compute the three side lengths with the distance formula.
\[(0,6)\text{ to }(-5,3): \sqrt{(-5)^2 + (-3)^2} = \sqrt{25+9} = \sqrt{34}\]
\[(0,6)\text{ to }(5,3): \sqrt{5^2 + (-3)^2} = \sqrt{25+9} = \sqrt{34}\]
\[(-5,3)\text{ to }(5,3): \sqrt{10^2 + 0^2} = 10\]
Two sides are equal and the third differs, so the triangle is isosceles but not equilateral. It is not right-angled either: \(34 + 34 = 68\), which is not \(10^2 = 100\).
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