What Would Be Life Without Tv, Internet, &Mobile
1. Find the distance between the points (a) (0, 2) and (3, 6) (b) (-2, 3) and (4, -5) © (2, -5) and (-3, 7)
2. Find the exact length of the interval between points (a) (2, 3) and (-1, 1) (b) (-1, 3) and (-7, 7)
3. Prove that the triangle with vertices (3, 4), (-2, 7) and (6, -1) is isosceles.
4. Show that the points (3, -4) and (8, 1) are equidistant from the point (7, -3).
5. Prove that the points X(2 , -3), Y(-1, 10 ) and Z(-6 , 5 ) all lie on a circle with centre at the origin.
6. If the distance between (a, -1) and (3, 4) is 5, find the value of a.
7. If the distance between (a, 3) and (4, 2) is 37 , find the values of a.
8. The points M(-1, -2), N(3, 0), P(4, 6) and Q(0, 4) form a quadrilateral. What type of quadrilateral is it?
Q. 9. For what value of m, the points (4, 3); (m, 1) and (1, 9) are collinear.
Q. 10. Prove that the diagonals of a rectangle bisect each other and are of equal length .Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
Q. 11. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).
Q. 12. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that x2 + y2 – 8x – 10y + 39 = 0
Q. 13. The line segment joining the points (3, – 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, – 2) and (5/3, q) respectively, find the value of p and q.
Q. 14. Find the centroid of the triangle whose vertices are (3, – 5); (– 7, 4) and (10, –
2. Find the exact length of the interval between points (a) (2, 3) and (-1, 1) (b) (-1, 3) and (-7, 7)
3. Prove that the triangle with vertices (3, 4), (-2, 7) and (6, -1) is isosceles.
4. Show that the points (3, -4) and (8, 1) are equidistant from the point (7, -3).
5. Prove that the points X(2 , -3), Y(-1, 10 ) and Z(-6 , 5 ) all lie on a circle with centre at the origin.
6. If the distance between (a, -1) and (3, 4) is 5, find the value of a.
7. If the distance between (a, 3) and (4, 2) is 37 , find the values of a.
8. The points M(-1, -2), N(3, 0), P(4, 6) and Q(0, 4) form a quadrilateral. What type of quadrilateral is it?
Q. 9. For what value of m, the points (4, 3); (m, 1) and (1, 9) are collinear.
Q. 10. Prove that the diagonals of a rectangle bisect each other and are of equal length .Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
Q. 11. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).
Q. 12. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that x2 + y2 – 8x – 10y + 39 = 0
Q. 13. The line segment joining the points (3, – 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, – 2) and (5/3, q) respectively, find the value of p and q.
Q. 14. Find the centroid of the triangle whose vertices are (3, – 5); (– 7, 4) and (10, –