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Do the points $P (1, 0)$, $Q (-5, 0)$ and $R (-2, 5)$ form a triangle ? If so, name the type of triangle formed.
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$PQ = \sqrt{(-5 - 1)^2 + (0 – 0)^2} = 6$ (I) (1 Mark)
$QR = \sqrt{(-2 + 5)^2 + (5 – 0)^2} = \sqrt{34}$ or $5.8$
$PR = \sqrt{(-2 - 1)^2 + (5 – 0)^2} = \sqrt{34}$ or $5.8$
Since sum of any two sides is greater than the third side, $\therefore$ Points $P, Q$ and $R$ form a triangle. (II) (1/2 Mark)
$QR = PR \Rightarrow PQR$ forms an isosceles triangle. (III) (1/2 Mark)
$QR = \sqrt{(-2 + 5)^2 + (5 – 0)^2} = \sqrt{34}$ or $5.8$
$PR = \sqrt{(-2 - 1)^2 + (5 – 0)^2} = \sqrt{34}$ or $5.8$
Since sum of any two sides is greater than the third side, $\therefore$ Points $P, Q$ and $R$ form a triangle. (II) (1/2 Mark)
$QR = PR \Rightarrow PQR$ forms an isosceles triangle. (III) (1/2 Mark)