(i) If a tree is to be planted exactly in the middle of the triangle PQR ie. at the centroid of ∆PQR to give shed to the people sitting in the lawn

Question

The students of Class X of a secondary school have been allotted a rectangular plot of land for their gardening activity. Saplings are being 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 figure. The students are to row seeds of the flowering plant on the remaining area of the plot.

(i) If a tree is to be planted exactly in the middle of the triangle PQR ie. at the centroid of ∆PQR to give shed to the people sitting in the lawn, then find the coordinates of the point where the tree should be planted.

(ii) What type of triangle is formed by the grassy lawn?

(iii) Find the area of the plot in which the students have to row the seeds.

OR 

If a special flowering plant has to be planted at a point which divides the line joining the points C and Q in the ratio 2:3, then find the coordinates of the point where this plant will be planted.

Answer 1

(i) P(3,3), Q(8,2), R(6,5)

Coordinates of required point are \(\left( \frac {3+8+6}{3},\frac {3+ 2+ 5}{3}\right)=\left(\frac {17}{3},\frac {10}{3}\right)\)

(ii) PR = QR = √13 

PQ = √26 

PQ² = PR² + QR² 

∴ ∆PQR is an isosceles right triangle

(iii) Area of the plot to row seeds = \(13 \times 9 - \frac {1}{2} \times \sqrt {13} \times \sqrt {13}\)

= 110.5 m²

OR

Coordinates of required point are