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Class 10 Maths extra questions for Coordinate Geometry




Given below are the Class 10 Maths extra questions and Important Questions for Coordinate Geometry
(a)Short answer type
(b)True or False statement
(c) Long answer questions
(d) Multiple Choice Questions

Short answer type

Question 1
Calculate the Following
  1. Distance between the point  (1,3) and ( 2,4)
  2. Mid-point of line segment  AB where A(2,5) and B( -5,5)
  3. Area of  the triangle  formed by joining the line segments (0,0)  ,( 2,0) and (3,0)
  4. Distance of point (5,0) from Origin
  5. Distance of point (5,-5) from Origin
  6. Coordinate of the point M which divided the line segment A(2,3) and B( 5,6) in the ratio 2:3
  7. Quadrant of the Mid-point of the line segment A(2,3) and B( 5,6)
  8.  the coordinates of a point A, where AB is the diameter of circle whose center is (2,−3) and B is (1, 4)
Solution
(a) $D=\sqrt{(1-2)^{2}+(3-4)^{2}}=\sqrt{2}$
(b)Mid-point is given by (2-5)/2,(5+5)/2 or (-3/2, 5)
(c) $A=\frac{1}{2}[0(0-0)+2(0-0)+3(0-0)]=0$
Since the three points are collinear, the area is zero
(d) $D=\sqrt{5^{2}+0^{2}}=5$
(e)$D=\sqrt{(-5)^{2}+0^{2}}=5$
(f) Coordinates of point M is given by
$x=\frac{2X3+3X2}{2+3}=\frac{12}{5}$
$y=\frac{2X6+3X5}{2+3}=\frac{27}{5}$
(g) Mid point is given by (7/2, 9/2) which lies in First quadrant
(h) We know that center is mid point of AB, So
$2=\frac{1+x}{2}$
$-3=\frac{4+y}{2}$
Solving these, we get (3,-10)

True or False statement

Question 2
(a) Point A( 0,0) B( 0,3) ,C( 0,7) and D( 2,0) formed a quadrilateral
(b) The point P (-2, 4) lies on a circle of radius 6 and center C (3, 5)
(c) Triangle PQR with vertices P (-2, 0), Q (2, 0) and R (0, 2) is similar to Δ XYZ with
Vertices X (-4, 0) Y (4, 0) and Z (0, 4).
(d) Point X (2, 2) Y (0, 0) and Z (3, 0) are not collinear
(e) The triangle formed by joining the point A( -3,0) , B( 0,0) and C( 0,2) is a right angle triangle
(f) A circle has its center at the origin and a point A (5, 0) lies on it. The point B (6, 8) lies inside the circle
(g) The points A (-1, -2), B (4, 3), C (2, 5) and D (-3, 0) in that order form a rectangle
Solution
  1. False, As three point are A,B and C are collinear, So no quadrilateral can be formed
  2. False, As the distance between the point P and C is $\sqrt{26}$ which is less than 6.So point lies inside the circle
  3. True. Both the triangle are equilateral triangle with side 4 and 8 respectively
  4. True. As the Area formed by the triangle XYZ is not zero
  5. True, If we plot the point on the Coordinate system, it becomes clear that it is right angle at origin
  6. False. The radius of the circle is 5 and distance of the point B is more than 5,So it lies outside the circle
  7. True. If we calculate the distance between two points, it becomes clear that opposite side are equal, also the diagonal are equal. So it is a rectangle

Long Answer Type

Question 1
Determine the ratio in which the point P (m, 6) divides the join of A (-4, 3) and B (2, 8). Also find the value of m.

Question 2
The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the co-ordinates of P and Q are (p, -2) and (5/3, q) respectively. Find the values of p and q.

Question 3
The line joining the points (2, 1) and (5, -8) is trisected at the points P and Q. If point P lies on the line 2x - y + K = 0. Find the value of K.

Question 4
A (4, 2), B (6, 5) and C (1, 4) are the vertices of ΔABC.
(i)The median from A meets BC in D. Find the co- ordinates of the point D.
(ii)Find the co- ordinates of point P on AD such that AD : PD = 2 : 1
(iii)Find the co- ordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1
(iv) What do you observe?

Question 5
If the points A (6, 1), B (8, 2), C (9, 4) and D (k, p) are the vertices of a parallelogram taken in order, then find the value of k and p.

Question 6
Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the co-ordinates of the third vertex.

Question 7
If C be the centroid of a triangle PQR and X be any other point in the plane, prove that
XP2+ XQ2 + XR2= CP2+CQ2+CR2+3CX2

Question 8
If P(x, y) is any point on the line joining the points A (a, 0), B (0, b), then show that x/a + y/b = -1 Question 9
If (-2, 3) (4, -3) and (4, 5) are the mid points of the sides of a triangle, find the co-ordinates of its centroid.

Question 10
Find the third vertex of a triangle, if two of its vertices are at (-3, 1) and (0, -2) and the centroid is at the origin.

Question 11
A (3, 2) and B (-2, 1) are two vertices of a triangle ABC whose centroid G has the co- ordinates [5/3,-1/3]. Find the co- ordinates of the third vertex C of the triangle.

Question 12
If D, E and F are the mid points of sides BC, CA and AB respectively of ΔABC, then testing co- ordinate geometry prove that
Area of ΔDEF =(1/4) &(Area of ΔABC)
Question 13
If A (4, 6), B (3, -2) and C (5, 2) are the vertices of ΔABC, then verify the fact that a median of a triangle ABC divides it into two triangles of equal areas.
Question 14
The area of a triangle is 5. Two of its vertices are (2, 1) and (3, 2). The third vertex lies on y = x + 3. Find the third vertex.
Question 15
Four points A (6, 3), B (-3, 5), C (4, -2) and D (x, 3x) are given in such a way that
$\frac {\Delta DBC}{\Delta ABC} = \frac {1}{2}$
find x.


Question 16
If three points (x1, y1), (x2, y2), (x3, y3) lie on the same line, prove that
$\frac {y_2 -y_3}{x_2x_3} + \frac {y_3 -y_1}{x_1x_3}+ \frac {y_1 -y_2}{x_2x_1}=0$

Question 17
Ifthe point P (m, 3) lies on the line segment joining the points A [-2/5, 6] and B (2, 8), find the value of m.
Question 18
If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a) then prove that x + y = a + b
Question 19
Find the value of a for which the area of the triangle formed by the points A (a, 2a), B (-2, 6) and C (3, 1) is 10 square units.
Question 20
If G be the centroid of a triangle ABC, prove that
AB2 + BC2 + CA2 = 3(GA2+ GB2+ GC2)
Question 21
Find the co-ordinates of circumcenter of a Δ ABC where A( 1, 2) ,B ( 3, -4) and C ( 5, -6 )
Question 22
The coordinates of the mid-point of the line joining the points (2p + 2, 3) and (4, 2q + 1) are (2p, 2q). Find the value of p and q.

Multiple Choice Questions

Question 1

The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is
(a) 14
(b) 28
(c) 8
(d) 6
Question 2
The points (�4, 0), (4, 0), (0, 3) are the vertices of a
(a) right triangle
(b) isosceles triangle
(c) equilateral triangle
(d) scalene triangle
Question 3
The point which divides the line segment joining the points (7, �6) and (3, 4) in ratio 1 : 2 internally lies in the
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant
Question 4
If the distance between the points (2, �2) and (�1, x) is 5, one of the values of x is
(a) �2
(b) 2
(c) �1
(d) 1



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Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20



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