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CBSE Class 10 Mathematics Worksheet

UNIT III: Coordinate Geometry - Coordinate geometry

Show that the points (a,a) (-a,-a) and $(-\sqrt{3}a, \sqrt{3}a)$ are the vertices of an equilateral triangle.

The vertices of triangle PQR are P(6,-2), Q(0,-6) and R(4,8). Find the coordinates of mid point of PQ, QR and PR.

Find the point on the x-axis which is equidistant from the points (2,-5) and (-2,9).

The ratio in which the point P (3/4, 5/12)divides the line segment joining the Points A (1/2, 3/2) and B (2, –5) is:

1:5

5:1

1:3

3:1

Prove that the point (3.0) (6,4) and (-1,3) are the vertices of a right angles isosceles triangle.

Prove that the points (7,10) (-2,5) and (3, -4) are the vertices of an isosceles right triangle.

Point A lies on the line segment PQ joining P(6,-6) and Q (-4,-1) in such a way that PA/PQ = 2/5. If point P also lies on the line 3x + K (y+1) = 0. Find the value of k.

Find the length of cirve X

$20\pi \sqrt{2}/3$ .

$15\pi /\sqrt{2}$ .

$60\pi /\sqrt{2}$ .

$20\pi /3$ .

Find the ratio in which the point P(3/4, 5/12) divides the line segment joining the point A(1/2, 3/2) and B(2,-5).

10.

If the point P(x,y) is equidistant from the points Q(a+b, b-a) and R(a-b, a+b), then prove that bx = ay.

11.

If A(2,-1), B(3,4), C(-2,3) and D(-3,-2) be four points in a plane, show that ABCD is a rhombus but not a square.

12.

Find the value of a, for which point P (a/3, 2) is the mid point of the line segment joining the points Q(-5, 4) and R(-1, 0)

13.

If A (5,2) B(2,-2) and C(-2,t) are the vertices of a right angle triangle with angle B = 90 degree, then find the value of t.

14.

If the value of abscissa of a point A is 0, where does the A lie on?

Origin

X-axis

Y-axis

None of the above

15.

Prove that the points P(0,-1), Q(-2,3) R(6,7) and S(8,3) are the vertices of a rectangle PQRS.

16.

The points A(4,7), B(P,3) and C(7,3) are the vertices of a right angled at B. Find the value of P.

17.

Find the mid point of side BC of triangle ABC, with A(1,-4) and the mid point of the sides through A being (2,1 ) and (0,-1).

18.

If the point C(-1, 2) divides internally the line segment joining the points A(2,5) and B(x,4) in the ratio 3:4. Find the value of $x^{2} + y^{2}$

19.

If the average of X, 2X+5, X+6 and 45 is 29, whats is "X"

20.

Find the ratio in which (-3, q) divides the line segment joining the points (-5,-4) and (-2, 3). Find the value of q.

CBSE Class 10 Mathematics Worksheet

UNIT III: Coordinate Geometry - Coordinate geometry

Answers

Since AB = BC = AC. Therefore ABC is an equilateral triangle.

Mid points PQ, QR and PR are D(3,-4), E(2,1) and F(5.3)

The point is (-7,0)

Option A

AB2 + CA2 = BC2, Pythagoras theorem is verified; right angles triangle.

ABC are the vertices of isosceles triangle

K= 18/5

Option B

1:5

10.

bx = ay

11.

All the four sides are equal

12.

a = -9

13.

t = 1

14.

Option C

Solution:

If abscissa or the x-coordinate is 0, it means the point lies on y-axis. So point A lies on y-axis.

15.

P, Q, R and S are the vertices of a rectangle PQRS

16.

P = 7 or 4

17.

midpoint of BC = (1,2)

18.

(x,y) = (-5) (-2); 29

19.

Option A

20.

q= 2/3

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