Math Olympiad Test: Coordinate Geometry- 2 - Class 9 MCQ

The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis. The point at which the two axes intersect is called the origin.

If P and Q have same abscissa but different ordinates then P and Q have coordinates, as P (a, c ), Q (a, b)
∵ x-coordinate is constant.
∴ P and Q will lie on line parallel to y-axis.

Minimum distance of point (α, b) from x-axis = Perpendicular distance between point and x-axis = |y-coordinate (ordinate) of the point| = |6| = 6

Point (4, 3) have (+, -) sign convention, that belongs to IV^th quadrant. 

Let the coordinates of point M be (0, k)
{∵ M is on y-axis}
∴ Coordinates of point N = (0, - K)
∴ Distance between point M and N
= |K - (-K)| = 2|K|

∵ (-3, -2) has (-, -) sign convention.
∴ (-3, -2)/0 Belongs to 3^rd quadrant.

Point A is the reflected point.
Point A will have coordinates, as, abscissa will not change and ordinate will change sign
∴ Reflected point will lie in 2^nd quadrant.

In ΔOAB
OA² = OB² + AB²
= (12)² + (OC)² = (12)² + (5)²
= 169
⇒ OA = √169 = 13 Units

On every point of y-axis, abscissa = 0
∴ x =  0 as the equation of y-axis

Coordinates of point Q ≡ (-3, 5).
After plotting ΔPOQ on graph, it can be clearly viewed that ΔPOQ is isosceles.
∴ Area of ΔPOQ = 1/2 × OR × PQ
= 1/2 × 5 × [3- (-3)]
= 1/2 × 5 × 6 = 15 sq. units

Distance between (-24, 10) and (48,10) will be equal to the absolute value of difference between the abscissa of the points as, the points have same ordinate.
∴ Distance = |48 - (-24)| = 72 units 

Ordinates of points are -6 and 3
∴ Difference = -6 - 3 = -9

Let the coordinates of point of intersection be (x₁, y₁)
∴ x₁ + y₁ = 6
x₁ - y₁ = 2
Solving these two equations, we get
x₁ = 4, and , y₁ = 2
∴ point of intersection  ≡ (4, 2)

In ΔOBC

BC² + OC² = OB²
⇒ (OA)² + (OC)² = OB²
⇒ (10)² + (24)² = OB²
⇒ OB = √676 = 26 units 

After plotting figure, it can be clearly seen that ABC is an isosceles triangle in which,  
AB = (6 - 2) = 4 units
CD = (6 - 0) = 6 units

∴ Ares of ΔABC = 1/2 × AB × CD
= 1/2 × 4 × 6 = 12 sq. units