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Exercise 13 - A

Q. 1. Find the distance between the points A (5, 4) and B (3, 5).

Q. 2. A (5, 6), B (-3, 0) and C (-1, 2) are the vertices of a triangle. What type of triangle is this.

Q. 3. If P (7, y), Q (2, 4) and R (6, 10) are three point such that PQ = PR. Find the value of y.

Q. 4. Show that the points (2, -4), (2, -1) and (1, -4) are the vertices of a right angled triangle.

Q. 5. The points P (x, y), Q (2, 4) and R (6, 10) are such that PQ = PR. Show that 2x + 3y = 29.

Q. 6. Show that the point (5, 0), (-2, -2), (0, 5) and (7, 7) taken in order form a rhombus.

Q. 7. The mid-point of the line joining (a, 2) and (3, 6) is (2, 6). Find the numerical value of a and b.

Q. 8. A point A is on the y-axis whose ordinate is 5 and B is a point (-3, 1). Calculate the length of AB.

Q. 9. Calculate the distance between the point P (2, 2) and Q (5, 4) correct to three significant figures.

Q. 10. The co-ordinates of the mid-point of the line segment PQ are (1, -2). The co-ordinates of P are (-3, 2). Find the co-ordinates of Q.

Q. 11. Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.

Q. 12. A (p, q), B (p + 3, q + 4), C (p – 1, q + 7) are the vertices of parallelogram ABCD. Find the co-ordinates of D.

Q. 13. Show that the point (-6, 1), (-3, 7), (7, 2) and (4, -4) are the vertices of a rectangle.

Q. 14. Show that the points A (-2, 0), B (1, -3) and C (-4, 2) are collinear.