# 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 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(x_{1}, y_{1}) = (4, 6), Q(x_{2}, y_{2}) = (3 , 2) and R (x_{3}, y_{3} ) = (6, 5)

Area of a triangle = 1/2 {x_{1} (y_{2} - y_{3}) + x_{2} (y_{3}- y_{1}) + x_{3} (y_{1} - y_{2})} ...Equation(1)

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

Area of triangle PQR = 1/2 [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]

= 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(x_{1}, y_{1}) = (12, 2) , Q(x_{2}, y_{2}) = (13, 6) and R(x_{3}, y_{3}) = (10,3)

Area of a triangle = 1/2 {x_{1} (y_{2} - y_{3}) + x_{2} (y_{3}- y_{1}) + x_{3} (y_{1} - y_{2})} ...Equation(1)

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

Area of triangle PQR = 1/2 [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]

= 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.

**Video Solution:**

## 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 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:

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. Hence, taking A as origin, the coordinates of the vertices are P, Q, and R are (4, 6), (3, 2), and (6, 5) respectively. and the coordinates of the vertices of ∆PQR, if C is the origin, is P(x_{1}, y_{1}) = (12, 2), Q(x_{2}, y_{2}) = (13, 6), Also the areas of the triangles in these cases is 9/2 Square units.