Co-ordinate Geometry
Question
Q1.
Write the coordinate of a point whose abscissa is -3 and ordinate is 2.
(a) (-3,0) (b) (-3,2) (c) (2,3) (d) (2,0)
Solution.
(b) (-3,2)
Note : abscissa represents x - coordinate. ordinate represents y - coordinate.
Solution
Q2.
Orthocentre, Circumcentre and Incentre coincide in ________ triangle.
Equilateral
Solution
Q3.
The point p(x,y) lies in the 2nd quadrant, which is greater x or y.
(a) y (b) x (c) x=y (d) None
Solution.
(a) y
Note : ordinate (y) is positive and abscissa is negative .
Solution
Q4.
Find the coordinates of the vertices of an equilateral triangle of side 4a as shown in figure (OA = 4a)
(a) (3√3a,a) (b) (a√3,a) (c) (a,2a) (d) (2a,2√3a)
Solution.
In triangle OMB
Using Pythagoras theorem
OB2 = OM2 + BM2
BM2 = OB2
- OM2
= (4a)2 - (2a)2
BM2 = 16a2 - 4a2 = 12a2
BM = 2√3a
Co-ordinate of B = (2a,2√3a)
Solution
Q5.
Find a point on x-axis which is equi-distance from A(2,-5) and B(-2,9).
(a) (5,-6) (b) (-7,0) (c) (-2,8) (d) (-2,0)
Solution.
We know that a point on x-axis is of the form R(x,0)
So, RA = RB
√(x - 2)2 + (0 + 5)2 =
√(x + 2)2 + (0 - 9)2
(x - 2)2 + 25 = (x + 2)2 + 81
x2 + 4 - 4x + 25 = x2 + 4 + 4x + 81
-8x = 56
x = -7
So, point is R (x,0) = R(-7,0)
Solution
Q6.
Two vertices of a triangle are (4,2) (9,5) and its centroid is at the origin, find the co-ordinate of the third vertex.
(a) (13,0) (b) (-13,-7) (c) (13,7) (d) (20,7)
Solution.
(b) (-13,-7)
Let third coordinate is (x,y)
(4 + 9 + 2)/3 = 0
13 + x = 0
x = -13
(2 + 5 + y)/3 = 0
7 + y = 0
y = -7
Solution
Q7.
Find the distance between the points (sinθ , cosθ) and (cosθ , sinθ)
(a) 2 (b) 1 (c) √2 (d) √3
Solution.
d = √(sinθ - cosθ)2 + (-cosθ - sinθ)2
= √sin2θ + cos2θ - 2sinθcosθ + cos2θ + sin2θ +
2sinθcosθ
= √2
Solution
Q8.
If three points (3,√3)(0,0)(3,a) form an triangle whose each angle is 600, find a.
(a) 1 (b) 2
(c) 3 (d) none of these
Solution.
(d) none of these
Solution
Q9.
Find the distance between the points (a2cos650 , 0)(0 , a2cos250).
(a) a4 (b) 2a (c) a (d) a2
Solution.
(d) a2
Solution
Q10.
The mid-point of the hypotenuse of a right angled triangle is equidistance from its vertices .
(a) No (b) Yes (c) Can't say
Solution.
(b) Yes
Solution
