Coordinate Geometry - Study Mode
[#6] Reflection of the point (4, -6) in the origin is:
Correct Answer
(C) (-4, 6)
Explanation
Solution: Reflection of point (4, -6) in origin is (-4, 6)
[#7] Find the equation of a circle whose diameter has end points (4, 3) and (-2, 1).
Correct Answer
(B) x 2 + y 2 - 2x - 4y = 5
Explanation
Solution: Go through option, Points (4, 3) and (-2, 1) will satisfy the equation from option B, x 2 + y 2 - 2x - 4y = 5
[#8] The graph of the equations 5x - 2y + 1 = 0 and 4y - 3x + 5 = 0, intersect at the point P(α, β). What is the value of (2α - 3β)?
Correct Answer
(A) 4
Explanation
Solution: $$eqalign{
& 5x - 2y = - 1,.,.,.,.,.,.,.,left( { ext{i}}
ight) imes 2 cr
& 4y - 3x = - 5,.,.,.,.,.,.,.,left( {{ ext{ii}}}
ight) cr
& 10x - 4y = - 2 cr
& underline {, - 3x + 4y = - 5,} cr
& 7x = - 7 cr
& x = - 1,,,y = - 2 cr
& 2alpha - 3x08eta cr
& = 2left( { - 1}
ight) - 3left( { - 2}
ight) cr
& = - 2 + 6 cr
& = 4 cr} $$
[#9] Area of the triangle formed by the graph of the straight lines x - y = 0, x + y = 2 and the x-axis is:
Correct Answer
(A) 1 sq unit
Explanation
Solution: Area of Δ formed by the graph x - y = 0, x + y = 2 and x-axis Intersection point of lines x - y = 0 and x + y = 2 will be (1, 1) ∴ Area bounded by lines x - y = 0, x - y = 2 and x-axis = $$frac{1}{2}$$ × 2 × 1 = 1 sq unit
[#10] The graph of 3x + 4y - 24 = 0 forms a triangle OAB with the co-ordinate axes, where O is the origin. Also the graph of x + y + 4 = 0 forms a triangle OCD with the coordinate axes. Then the area of ΔOCD is equal to:
Correct Answer
(B) $$frac{1}{3}$$ of area of ΔOAB
Explanation
Solution: $$eqalign{
& 3x + 4y - 24 = 0 cr
& Rightarrow 3x + 4y = 24 cr
& Rightarrow frac{{3x}}{{24}} + frac{{4y}}{{24}} = 1 cr
& Rightarrow frac{x}{8} + frac{y}{6} = 1 cr
& { ext{Area of }}Delta OAB = frac{1}{2} imes 6 imes 8 = 24{ ext{ sq}}{ ext{. units}} cr
& { ext{And,}} cr
& x + y + 4 = 0 cr
& Rightarrow x + y = - 4 cr
& Rightarrow frac{x}{{left( { - 4}
ight)}} + frac{y}{{left( { - 4}
ight)}} = 1 cr} $$ $$eqalign{
& { ext{Area of }}Delta OCD = frac{1}{2} imes 4 imes 4 = 8{ ext{ sq}}{ ext{. units}} cr
& herefore { ext{Area of }}Delta OCD = frac{1}{3}{ ext{Area of }}Delta OAB cr} $$