NCERT Solutions Class 10 Mathematics Chapter Download 7 Coordinate Geometry In Pdf
Question 1. Find the distance between the following pairs of points :
(i) (2, 3), (4, 1)
(ii) (β 5, 7), (β 1, 3)
(iii) (a, b), (β a, β b)
Question 2. Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
Question 3. Determine if the points (1, 5), (2, 3) and (β 2, β 11) are collinear.
Question 4. Check whether (5, β 2), (6, 4) and (7, β 2) are the vertices of an isosceles triangle.
Question 5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, βDonβt you think ABCD is a square?β Chameli disagrees. Using distance formula, find which of them is correct.
Question 6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) (β 1, β 2), (1, 0), (β 1, 2), (β 3, 0)
(ii) (β3, 5), (3, 1), (0, 3), (β1, β 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Question 7. Find the point on the x-axis which is equidistant from (2, β5) and (β2, 9).
Question 8. Find the values of y for which the distance between the points P(2, β 3) and Q(10, y) is 10 units
Question 9. If Q(0, 1) is equidistant from P(5, β3) and R(x, 6), find the values of x. Also find the distances QR and PR.
Question 10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (β 3, 4).
Question 1. Find the coordinates of the point which divides the join of (β1, 7) and (4, β3) in the ratio 2 : 3.
Question 2. Find the coordinates of the points of trisection of the line segment joining (4, β1) and (β2, β3).
Question 3. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs 1 4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1 5 th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Question 4. Find the ratio in which the line segment joining the points (β 3, 10) and (6, β 8) is divided by (β 1, 6).
Question 5. Find the ratio in which the line segment joining A(1, β 5) and B(β 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
Question 6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Question 7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, β 3) and B is (1, 4).
Question 8. If A and B are (β 2, β 2) and (2, β 4), respectively, find the coordinates of P such that AP = 3 AB 7 and P lies on the line segment AB.
Question 9. Find the coordinates of the points which divide the line segment joining A(β 2, 2) and B(2, 8) into four equal parts.
Question 10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (β 1, 4) and (β 2, β 1) taken in order. [Hint : Area of a rhombus = 1 2 (product of its diagonals)]
Question 1. Find the area of the triangle whose vertices are :
(i) (2, 3), (β1, 0), (2, β 4)
(ii) (β5, β1), (3, β5), (5, 2)
Question 2. In each of the following find the value of βkβ, for which the points are collinear.
(i) (7, β2), (5, 1), (3, k)
(ii) (8, 1), (k, β 4), (2, β5)
Question 3. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, β1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
Question 4. Find the area of the quadrilateral whose vertices, taken in order, are (β 4, β 2), (β 3, β 5), (3, β 2) and (2, 3).
Question 5. You have studied in Class IX, (Chapter 9, Example 3), that a median of a triangle divides it into two triangles of equal areas. Verify this result for Ξ ABC whose vertices are A(4, β 6), B(3, β2) and C(5, 2).
Question 1. Determine the ratio in which the line 2x + y β 4 = 0 divides the line segment joining the points A(2, β 2) and B(3, 7).
Question 2. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
Question 3. Find the centre of a circle passing through the points (6, β 6), (3, β 7) and (3, 3).
Question 4. The two opposite vertices of a square are (β1, 2) and (3, 2). Find the coordinates of the other two vertices.
Question 5. The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the Fig. 7.14. The students are to sow seeds of flowering plants on the remaining area of the plot.
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of Ξ PQR if C is the origin? Also calculate the areas of the triangles in these cases. What do you observe?
Question 6. The vertices of a Ξ ABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that AD AE 1 AB AC 4 = Calculate the area of the Ξ ADE and compare it with the area of Ξ ABC. (Recall Theorem 6.2 and Theorem 6.6).
Question 7. Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Ξ ABC.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1. (iv) What do yo observe?
[Note : The point which is common to all the three medians is called the centroid and this point divides each median in the ratio 2 : 1.]
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