If the coordinates of a point M are (-2, 9) which can also be expressed as $(1 + x, y^{2})$ and y > 0, then find in which quadrant do the following points lie : P(y, x), Q(2, x), $R (x^{2}, y - 1)$ , S(2x, -3y).

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Solution

Here, M(-2, 9) can also be expressed as $(1 + x, y^{2})$

$∴ (1 + x, y^{2}) \Leftrightarrow (- 2, 9) and y > 0$

$\Rightarrow 1 + x = - 2 and y^{2} = 9$

$\Rightarrow x = - 3 and y = \sqrt{9} = 3 (∵ y > 0)$

$P (y, x) = P (3, - 3)$ it lies in IV quadrant

$Q (2, x) = Q (2, - 3),$ also lies in IV quadrant

$R (x^{2}, y - 1) = R ((- 3)^{2}, 3 - 1) = R (9, 2),$ it lies in I quadrant

$S (2 x, - 3 y) = S (2 \times (- 3), - 3 \times 3) = S (- 6, - 9),$ it lies in III quadrant

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