Math Olympiad Test: Coordinate Geometry- 1 - Class 9 MCQ

x-axis and y-axis divide the plane in 4 quadrants.

Every point on x-axis is of the form (x, 0)
∴ ordinate of any point on x-axis = 0

Sign convention for Quadrants are
I^st quadrant → (+, +)
II^nd quadrant → (-, +)
III^rd quadrant → (-, -)
IV^th quadrant → (+, -)
∴ Required point will lie in II or III quadrant.

O is the centre of circle and A is the point of tangency.
∵ Point of tangency lies on x -axis
∴ Ordinate of point = 0

Perpendicular distance from y-axis
= |abscissa| = |-11| = 11

If  abscissa = ordinate, i.e, x = y then using this relation in equation of line, we have
x = 3x + 2 ⇒ x = -1
∴ Point has coordinates = (-1, -1)
Point has sign convection of (-, -)
∴ Point will lie in 3^rd quadrant 

Area of PQR = 1/2 × PQ × QR
= 1/2 × 4 × 3 = 6 (units)²

∵ Centroid of any D lies within it, and all the coordinates A, B and C are in I^st quadrant (Positive)
∴ centroid will lie in I^st quadrant.

Point A is 3 units above x-axis.
∴ Its mirror image will be 3 units below x-axis, and the x-coordinate will remain constant
∴ Coordinates of point B ≡ (4, -3)

When ordinate = abscissa, then y = x
∴ 2x + 3x = 5
⇒ 5x = 5
⇒ x = 1
∴ x = y = 1 will be point on line having equal abscissa and ordinate
∴ Point P = (1, 1)
∴ Its image about y-axis will be (-1, 1).