Coordinate Geometry - Study Mode

[#61] The point P(5, -2) divides the segment joining the point (x, 0) and (0, y) in the ratio 2 : 5 what is the value of x and y?
Correct Answer

(C) x = 7, y = -7

Explanation

Solution: $$eqalign{
& left( {x,,y}
ight) = left( {frac{{{m_1}{x_2} + {m_2}{x_1}}}{{{m_1} + {m_2}}},,frac{{{m_1}{y_2} + {m_2}{y_1}}}{{{m_1} + {m_2}}}}
ight) cr
& 5 = frac{{2 imes 0 + 5 imes x}}{{2 + 5}} cr
& 35 = 5x cr
& x = 7 cr
& - 2 = frac{{2 imes y + 5 imes 0}}{{2 + 5}} cr
& - 14 = 2y cr
& y = - 7 cr
& x = 7,,y = - 7 cr} $$

[#62] What is the equation of line whose slope is $$frac{{ - 1}}{2}$$ and passes through the intersection of the lines x - y = -1 and 3x - 2y = 0?
Correct Answer

(A) x + 2y = 8

Explanation

Solution: Given, Equation of the lines: x - y = -1 . . . . . . (i) 3x - 2y = 0 . . . . . . (ii) From equation (i) & (ii) Intersecting co-ordinate (x 1 , y 1 ) = (2, 3) m = $$frac{{ - 1}}{2}$$ given Now, Required equation of the line = y - y 1 = m(x - x 1 ) = y - 3 = $$frac{{ - 1}}{2}$$ (x - 2) x + 2y = 8

[#63] What will be the equation of the perpendicular bisector of segment joining the points (5, -3) and (0, 2)?
Correct Answer

(D) x - y = 3

Explanation

Solution: $$eqalign{
& { ext{O is mid point of AB}} cr
& x = frac{{5 + 0}}{2} = frac{5}{2} cr
& y = frac{{ - 3 + 2}}{2} = frac{{ - 1}}{2} cr
& { ext{Slope of AB }}left( {{m_1}}
ight) cr
& = frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} cr
& = frac{{2 - left( { - 3}
ight)}}{{0 - 5}} cr
& = frac{5}{{ - 5}} cr
& = - 1 cr} $$ Slope of (m 2 ) CD = 1 [lines are perpendicular to each other] m 1 × m 2 = -1 Equation of line $$eqalign{
& left( {y + frac{1}{2}}
ight) = 1left( {x - frac{5}{2}}
ight) cr
& Rightarrow 2left( {x - y}
ight) = 6 cr
& Rightarrow x - y = 3 cr} $$

[#64] What is the equation of a circle with centre of origin and radius is 6 cm?
Correct Answer

(D) x 2 + y 2 - 36 = 0

Explanation

Solution: (x - a) 2 + (y - b) 2 = r 2 Origin point = (0, 0) (x - 0) 2 + (y - 0) 2 = 6 2 x 2 + y 2 = 36 x 2 + y 2 - 36 = 0

[#65] Point A divides segment BC in the ratio 4 : 1 Co-ordinates of B are (6, 1) and C are $$left( {frac{7}{2},,6}
ight).$$ xa0What are the co-ordinates of point A?
Correct Answer

(B) (4, 5)

Explanation

Solution: $$eqalign{
& x = frac{{4 imes frac{7}{2} + 1 imes 6}}{{4 + 1}} Rightarrow 4 cr
& y = frac{{4 imes 6 + 1 imes 1}}{{4 + 1}} Rightarrow 5 cr
& { ext{A}}left( {4,,5}
ight) cr} $$