# 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 ∆ PQR if C is the origin? Also calculate the areas of the triangles in these cases. What do you observe?

**Solution:**:

(i) Taking A as origin, we will take AD as the x-axis and AB as the y-axis.

It can be observed from the figure that the coordinates of point P, Q, and R are (4, 6), (3, 2), and (6, 5) respectively.

Let P(x₁, y₁) = (4, 6), Q(x₂, y₂) = (3 , 2) and R (x₃, y₃ ) = (6, 5)

Area of a triangle = 1/2 [x₁ (y₂ - y₃) + x₂ (y₃- y₁) + x₃ (y₁ - y₂)] .....(1)

By substituting the values of vertices P, Q, R in the Equation (1),

Area of triangle PQR = 1/2 [x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)]

= 1/2 [4(2 - 5) + 3(5 - 6) + 6(6 - 2)]

= 1/2 [-12 - 3 + 24]

= 9/2 square units

(ii) Taking C as origin, CB as x-axis, and CD as the y-axis

The coordinates of vertices P, Q, and R are (-12, -2), (-13, -6), and (-10, -3) respectively.

Let P(x₁, y₁) = (-12, -2) , Q(x₂, y₂) = (-13, -6) and R(x₃, y₃) = (-10, -3)

Area of a triangle = 1/2 [x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)] .....(1)

By substituting the values of vertices P, Q, R in the Equation (1),

Area of triangle PQR = 1/2 [x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)]

= 1/2 [-12(-6 + 3) - 13(-3 + 2) - 10(-2 + 6)]

= 1/2 [36 + 13 - 40]

= 9/2 square units

It can be observed that the area of the triangle is the same in both cases.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 7

**Video Solution:**

## 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 ∆ PQR if C is the origin? Also calculate the areas of the triangles in these cases. What do you observe?

Maths NCERT Solutions Class 10 Chapter 7 Exercise 7.4 Question 5

**Summary:**

The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the above figure. The students are to sow seeds of flowering plants on the remaining area of the plot. (i) aking A as origin, the coordinates of the vertices are P, Q, and R are (4, 6), (3, 2), and (6, 5) respectively and (ii) The coordinates of the vertices of ∆PQR, if C is the origin, are P, Q, and R are (-12, -2), (-13, -6), and (-10, -3). Also, the areas of the triangles in both cases are 9/2 square units.

**☛ Related Questions:**

- 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).
- Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
- Find the centre of a circle passing through the points (6, - 6), (3, - 7) and (3, 3).
- The two opposite vertices of a square are (- 1, 2) and (3, 2). Find the coordinates of the other two vertices.

visual curriculum