## Co ordinate geometry Questions

__section A__

**Q.1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).**

**Q.2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the ratio 3: 4.**

**Q.3. Show that the points (1, 1), (3, -2) and (-1, 4) are collinear.**

**Q.4. Find the centroid of the triangle whose vertices are (3, -5); (- 7, 4) and (10, - 2).**

**Q.5. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7)**

**Q.6. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.**

**Q.7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).**

**Q.8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.**

**Q.9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x1, y1), B(x2, y2) and C(x3, y3) are given by (x1+x2+x3)/3 , (y1+y2+y3)/3**

**Q.10. Prove that the diagonals of a rectangle bisect each other and are of equal length.**

__Section-B__**Choose the correct answer from the given four options:**

**1. The distance of the point P (2, 3) from the x-axis is**

**(A) 2 (B) 3 (C) 1 (D) 5**

**2. The distance between the points A (0, 6) and B (0, –2) is**

**(A) 6 (B) 8 (C) 4 (D) 2**

**3. The distance of the point P (–6, 8) from the origin is**

**(A) 8 (B) 2 √7 (C) 10 (D) 6**

**4. The distance between the points (0, 5) and (–5, 0) is**

**(A) 5 (B) 5√ 2 (C) 2 √5 (D) 10**

**5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is**

**(A) 5 (B) 3 (C) √ 34 (D) 4**

__Section-C__

**1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).**

**2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the ratio 3: 4.**

**3. Show that the points (1, 1), (3, - 2) and (- 1, 4) are collinear.**

**4. Find the centroid of the triangle whose vertices are (3, - 5); (- 7, 4) and (10, - 2).**

**5. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y**

**6. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7)**

**7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).**

**8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.**

**9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x1, y1), B(x2, y2) and C(x3, y3) are given by [(x1+x2+x3)/3] , [ )y1+y2+y3)/3]**

**10. Prove that the diagonals of a rectangle bisect each other and are of equal length**

**11. 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.**

**12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).**

**13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis respectively, find the coordinates of the vertices of the square PQRS.**

**14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that x 2 + y2 - 8x -10y + 39 = 0**

**15. 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.**

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Sample paper 1

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