CBSE Class 10 Mathematics Coordinate Geometry Assignment Set 17

Question. In what ratio does the point \( (3,3) \) divide the line segment joining the points \( (2,4) \) and \( (4,2) \) ?
Answer: \( 1:1 \)

Question. In what ratio does the point \( (3,-2) \) divide the line segment joining the points \( A (2,-1) \) and \( B (7,-6) \) ?
Answer: \( 1:4 \)

Question. In what ratio is the line segment joining the points \( A (-3,2) \) and \( B (5,6) \) divided by \( y \)-axis ?
[Hint: let ratio be \( k:1 \), Find Co-ordinates then Put \( x \)-Co-ordinate \( = 0 \), find \( k \)]
Answer: \( 3:5 \)

Question. Find the ratio in which the join of \( A(5,6) \) and \( B(7,-8) \) is divided by \( x \)-axis
Answer: \( 3:4 \)

Question. Find the ratio in which the line \( 3x+y=9 \) divides the segment joining the points \( (1,3) \) and \( (2,7) \)
Answer: \( 3:4 \)

Question. By using section formula, Show that the points \( (1,1) \), \( (3,-2) \), and \( (-1,4) \) are Collinear.
Answer: —

Question. Find the Co-ordinates of the Centre of a circle of the largest chord whose Co-ordinates are \( A(-1,2) \) and \( B(5,6) \)
Answer: \( (2,4) \)

Question. Find the Co-ordinates of a point where the diagonals of a parallelogram formed by joining the points \( A(6,1) \), \( B(8,2) \), \( C(9,4) \) and \( D(7,3) \) meet.
Answer: \( \left(\frac{15}{2}, \frac{5}{2}\right) \)

Question. Find the ratio in which the line \( x-y=2 \) divides the line segment joining the points \( (3,-1) \) and \( (8,9) \)
Answer: \( 2:3 \)

Question. Find the Centre of a circle passing through the points \( (6,-6) \), \( (3,-7) \) and \( (3,3) \)
Answer: \( (3,-2) \)