Assignments class 10 Chapter Co-Ordinate

Q1. Find the distance between the following points:

(a) A(3 , 5) and B(8 , – 7) (b)P( a + b , a – b ) and Q ( a– b , –a – b )

Q2. Find the value of x for which the distance between points A(x, 7) and B (–2, 3) is 4√5 units.

Q3. If the points (3, 2) and (2, –3) are equidistant from points (x, y) show that x + 5y = 0.

Q4. Show that the following points are collinear:
(a) (–5, 6), (–1, 2) and (2, –1)
(b) (4, 3) , (5,1 ) and (1, 9)

Q5. Show that following points are vertices of right triangle. Also, name the right angle.
(a)(4, 4) , ( 3 , 5) , (–1 ,1)
(b)(–2, 3) , ( 8, 3) , ( 6, 7)

Q6. Show that following points are vertices of a rectangle:
(a) (2 , –2) , ( 8, 4) , ( 5, 7 ) , (– 1, 1)
b)(–4 , –1) , (–2 , 4) , ( 4, 0 ) , ( 2, 3 )

Q7. Show that following points are vertices of a square:
a) ( 0 , –1) , ( 2, 1) , ( 0, 3) , (–2, 1)
(b)( 0, 1) , ( 1, 4) , ( 4,3) , ( 3, 0)

Q8. Show that following points are vertices of rhombus:

(a) ( 0, 5 ) , (–2, –2 ) , ( 5 , 0 ) , ( 7, 7 ) (b ) ( 2, –1) , ( 3, 4) , (–-2, 3) , (–3 , –2)

Q9. Show that the points ( a, a ) , (–a, –a ) and (–√3 a , √3 a) form an equilateral triangle.

Q10. Find the co-ordinates of circumcenter of a ∆ ABC where A( 1, 2) ,B ( 3, –4) and C ( 5, –6 ).

Q11. Find radius of the circle, the co-ordinates of the ends of whose diameter are (–1, 2) and (3, –4 ).

Q12. (a) Find the point on x-axis, which is equidistant from points ( 7, 6 ) and ( 9 , 4 ).

(b)Find the point on y-axis, which is equidistant from points ( 5, 2 ) and (–4 , 3 ).

Q13. A point P is at a distance of√10 from the point ( 4, 3). Find the co-ordinates of P, if its ordinate is twice its abscissa.

Q14. A line of length 10 units has (–-2, 3) as one of its end points. If the ordinate of the other end be 9, Show that its abscissa is 6 or–10.

Q15. The opposite angular points of a square be ( 3, 4 ) and ( 1, –1). Find the co-ordinates of the remaining angular points.

Answers

Ans 1 . (a) 13, (b) 2 √a² + b²

Ans 2. 6 or – 10

Ans 10. (11, 2)

Ans11.√13

Ans12. (a) (3, 0)(b ) (0, 15)

Ans13. (3, 6)

Ans15. (9/2, 1/2) and (–1/2 , 5/2 )