Three points A(1, −2) B(3, 4) and C(4, 7) form

(a) a straight line
(b) an equilateral triangle
(c) a right-angled triangle
(d) None of these

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Solution

(a) a straight line
The given points are A(1, −2), B(3, 4) and C(4, 7).
Here, $(x_{1} = 1, y_{1} = - 2), (x_{2} = 3, y_{2} = 4) and (x_{3} = 4, y_{3} = 7)$ .
Therefore,
$Area of ∆ A B C = \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]$

$= \frac{1}{2} [1 (4 - 7) + 3 (7 + 2) + 4 (- 2 - 4)] = \frac{1}{2} [- 3 + 27 - 24] = 0$
Thus, the given points are collinear, i.e. they form a straight line.

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