NCERT class 10 maths chapter 7 Coordinate Geometry
Question 1:Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).
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Question 2:Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
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Question 3:Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3).
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Question 4:The two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of the other two vertices.
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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 D PQR if C is the origin? Also calculate the areas of the triangles in these cases. What do you observe?
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Question 6:The vertices of a D 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 D ADE and compare it with the area of D ABC. (Recall Theorem 6.2 and Theorem 6.6).
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Question 7:Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of D 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.] (v) If A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of D ABC, find the coordinates of the centroid of the triangle.
Question 8:ABCD is a rectangle formed by the points A(–1, –1), B(– 1, 4), C(5, 4) and D(5, – 1). P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.