CBSE Class 10 Mathematics Coordinate Geometry Assignment Set 18

Question. The Co-ordinate of the centre of a circle is \( (2, 3) \). If the co-ordinate of one end of the largest chord is \( (5, 7) \). Find the other co-ordinate of the chord
Answer: \( (-1, -1) \)

Question. The vertices of a triangle are \( A(3,4) \) \( B(7, 2) \) and \( C(-2, -5) \). Find the length of the median through the vertex \( A \).
Answer: \( \sqrt{122}/2 \text{ Units} \)

Question. Find the co-ordinate of a point which is three-fourth of the way from \( (3, 1) \) to \( (-2, 5) \)
Answer: \( \left(-\frac{3}{4}, 4\right) \)

Question. The mid points of the sides of a triangle are \( A(2,1) \), \( B(1,0) \) and \( C(-1,3) \). Find the Co-ordinates of the vertices of the triangle.
Answer: \( (0,4), (4,-2), (-2,2) \)

Question. Find the Co-ordinates of the points which divide the line segment joining \( A(5,-6) \) and \( B(7,-8) \) into four equal parts
Answer: \( C\left(\frac{11}{2}, -\frac{13}{2}\right), D(6, -7), E\left(\frac{13}{2}, -\frac{15}{2}\right) \)

Question. If \( A \) and \( B \) are \( A(-3,2) \); \( B(5,6) \) respectively, find the Co-ordinates of \( P \) such that \( AP = \frac{2}{7} AB \) and \( P \) lies on the line segment \( AB \). [Hint: Find ratio \( AP:PB \) then proceed]
Answer: \( \left(-\frac{5}{7}, \frac{22}{7}\right) \)

Question. Find the area of an equilateral triangle whose vertices are \( A(-3,0) \) \( B(3,0) \) and \( C(0, 3\sqrt{3}) \) [Hint: \( \Delta = \frac{\sqrt{3}}{4} \text{side}^2 \)]
Answer: \( 9\sqrt{3} \text{ Sq. Units} \)

Question. Find the area of a rhombus whose Co-ordinates are \( A(0,5) \), \( B(-2,-2) \), \( C(5,0) \) and \( D(7,7) \) [Hint: area \( = \frac{1}{2} \) product of diagonals]
Answer: \( 45 \text{ sq units} \)

Question. Find the area of a square whose Co-ordinates are \( A(3,2) \), \( B(0,5) \), \( C(-3,2) \) and \( D(0,1) \)
Answer: \( 18 \text{ sq units} \)

Question. Find \( p \) and \( q \) if \( A(2, p) \), \( B(5,4) \), \( C(4,7) \) and \( D(q,4) \) are the vertices of a parallelogram.
Answer: \( p = 1, q = 1 \)