Coordinate Geometry_8

1. Find the distance between \( P(x, y) \) and \( Q(a, b) \).[1U]
2. Write the formula to find the distance between the points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \).[1U]
3. Find the distance between the points \( (k, 0) \) and \( (0, k) \).[1U]
4. What will be the \( y \)-coordinate of any point lying on the \( x \)-axis?[1U]
5. In which quadrant does the point \( (8, -5) \) lie?[1K]
6. In which quadrant does the point \( (-5, 2) \) lie?[1K]
7. Find the distance between the points \( A(-3, -4) \) and \( O(0, 0) \).[1U]
8. Find the distance between the points \( (-a, 0) \) and \( (0, -b) \).[1U]
9. If the distance between the points \( A(0, 9) \) and \( B(x, 0) \) is 15 units, find the value of \( x \).[2U]
10. Find the distance between the points \( P(2, 3) \) and \( Q(5, 7) \).[1U]
11. Find the distance between the points \( (-a, a) \) and \( (2a, 5a) \).[1U]
12. If \( AB \), \( BC \), and \( AC \) are the sides of a right-angled \( \triangle ABC \), then express \( AC \) in terms of \( AB \) and \( BC \).[1U]
13. In the adjoining figure, \( \angle B = 90^\circ \), \( AB = 4 \, \text{cm} \), and \( BC = 3 \, \text{cm} \). Find the length of \( AC \).[2U]
14. The \( x \)-coordinate of a point \( A \), which lies on the \( x \)-axis, is \( -8 \); and \( y \)-coordinate of a point \( B \), which lies on the \( y \)-axis, is 6. Find the length of line segment \( AB \).[1U]
15. In the given figure, what is the distance of the point \( P \) from the origin?[1U]
16. Find the distance from the origin to point \( (-6, -8) \).[2U]
17. Find the distance between the points \( A(4, 5) \) and \( B(-4, -5) \).[2U]
18. If the distance between the points \( P(0, 6) \) and \( Q(a, 0) \) is 6 units, then find the value of \( a \).[2U]
19. If the distance between the points \( A(1, -2) \) and \( B(x, -6) \) is \( \sqrt{32} \), then find the value of \( x \).[2U]
20. Prove that the following given points are collinear: \( (3, -1), (1, 1), (-2, 4) \).[2HA]
21. Prove that the following given points are collinear: \( (5, 1), (3, 2), (1, 3) \).[2HA]
22. Find the length of side \( AB \) from the given right-angled triangle.[2U]
23. Determine whether the numbers 6, 8, 10 are Pythagorean triples or not.[2HA]
24. In alongside figure, find the value of \( x \).[2U]
25. A pencil of 13 cm length is kept inside the cylindrical glass as shown in figure. Find the height of the glass if its diameter is 4 cm.[2U]
26. Find the value of \( x \) in the given figure.[2U]
27. In the adjoining figure, find the value of \( PS \).[2U]
28. Find the length of \( AC \) from the given figure of kite.[2U]