Question

The points (1, -1), $(-\frac{1}{2},\frac{1}{2})$ and (1, 2) are the vertices of an isosceles triangle

Say yes or no.

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient

Answer 1

Answer: (A)

Yes

Let the point (1, -1), $(-\frac{1}{2},\frac{1}{2})$ and (1, 2) be denoted by P, Q and R respectively
Now PQ = $\sqrt{{(-\frac{1}{2}-1)}^2+{(\frac{1}{2}+1)}^2}=\sqrt{\frac{18}{4}}=\frac{3}{2}\sqrt{2}$
QR = $\sqrt{{(1+\frac{1}{2})}^2+{(2-\frac{1}{2})}^2}=\sqrt{\frac{18}{4}}=\frac{3}{2}\sqrt{2}$
PR = $\sqrt{{(1-1)}^2+{(2+1)}^2}=\sqrt{9}=3$
From the above we see that PQ = QR
$\therefore$ The triangle is isosceles