**NCERT Solution For Class 10, Maths, Chapter 7 Coordinate Geometry, Exercise 7.4** is an optional exercise which has final conclusion of all concept which has learnt in earlier exercise. Students must study all the questions present in this exercise to clear all the fundaments.

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Toggle## Class 10, Maths, Chapter 7, Exercise 7.4 Solutions

**Q.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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**Q.2. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.**

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**Q.3. Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3).**

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**Q.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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**Q.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 Δ PQR if C is the origin?**

**Also calculate the areas of the triangles in these cases. What do you observe?**

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**Q.6. The vertices of a Δ 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 $\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}$. Calculate the area of the Δ ADE and compare it with the area of Δ ABC. (Recall Theorem 6.2 and Theorem 6.6). **

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**Q.7. Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Δ 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(x _{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) are the vertices of Δ ABC, find the coordinates of **

**the centroid of the triangle.**

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**Q.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.**

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