Coordinate Geometry - Study Mode

[#46] For triangle PQR, find equation of altitude PS if co-ordinates of P, Q and R are (1, 2), (2, -1) and (0,5) respectively?
Correct Answer

(C) x - 3y = -5

Explanation

Solution: Given, P(1, 2), Q(2, -1) and R(0, 5) Slope of line QR (m 1 ) $$ = frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = frac{{5 - left( { - 1}
ight)}}{{0 - 2}} = - 3$$ If the lines are perpendicular then product of slopes is equal to -1 m 1 × m 2 = -1 -3 × m 2 = -1 m 2 = $$frac{1}{3}$$ ∴ Equation of line passes through the point (1, 2) whose slope (m 2 ) = $$frac{1}{3}$$ y - y 1 = m 2 (x - x 1 ) y - 2 = $$frac{1}{3}$$(x - 1) y - $$frac{1}{3}$$x = 2 - $$frac{1}{3}$$ 3y - x = $$frac{5}{3}$$ × 3 x - 3y = -5

[#47] What is the reflection of the point (5, -3) in the line y = 3?
Correct Answer

(B) (5, 9)

[#48] The point Q(a, b) is first reflected in y-axis to Q 1 and Q 1 is reflected in x-axis to (-5, 3). The co-ordinates of point Q are
Correct Answer

(D) (5, -3)

Explanation

Solution: If Q 2 (-5, 3) is first reflected in x-axis then it goes in III rd quadrant Q 1 (-5, -3) If Q 1 is reflected in y-axis to Q(5, -3)

[#49] The straight line y = 3x must pass through the point:
Correct Answer

(A) (0, 0)

Explanation

Solution: y = 3x must pass through the point (0, 0) because only this point satisfies the equation.

[#50] Point P(-2, 5) is the midpoint of segment AB. Co-ordinates of A are (-5, y) and B are (x, 3). What is the value of x?
Correct Answer

(A) 1

Explanation

Solution: $$eqalign{
& Rightarrow { ext{mid point co - ordinate}}left( {frac{{ - 5 + x}}{2},,frac{{y + 3}}{2}}
ight) cr
& Rightarrow frac{{ - 5 + x}}{2} = - 2 cr
& Rightarrow - 5 + x = - 4 cr
& Rightarrow x = 1 cr} $$