A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants.

Question

A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above situation, the gardener took help from the students of class 10. They made a chart for it which looks like the given figure.

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Based on the above, answer the following questions:
(i) If $A$ is taken as origin, what are the coordinates of the vertices of $	riangle PQR$?
(ii) (b) Find the coordinates of the point which divides the line segment joining points $P$ and $R$ in the ratio $2 : 1$ internally.
(iii) Find out if $	riangle PQR$ is an isosceles triangle.

Accepted Answer

Step 1: (i) $P(4, 6)$, $Q(3, 2)$, $R(6, 5)$
Step 2: (ii)(b) Using section formula, point dividing $PR$ in ratio $2 : 1$: $\left(\frac{2 	imes 6 + 1 	imes 4}{3}, \frac{2 	imes 5 + 1 	imes 6}{3}ight) = \left(\frac{16}{3}, \frac{16}{3}ight)$
Step 3: (iii) $PQ = \sqrt{17}$, $QR = \sqrt{18}$, $PR = \sqrt{5}$. Since $PQ 
eq QR 
eq PR$, $	riangle PQR$ is not isosceles.

Question

Solution