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) (a) Find distances $PQ$ and $QR$.
OR
(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)(a) $PQ = \sqrt{(4 - 3)^2 + (6 - 2)^2} = \sqrt{1 + 16} = \sqrt{17}$
Step 3: $QR = \sqrt{(3 - 6)^2 + (2 - 5)^2} = \sqrt{9 + 9} = \sqrt{18}$
Step 4: (iii) $PR = \sqrt{(4 - 6)^2 + (6 - 5)^2} = \sqrt{4 + 1} = \sqrt{5}$. Since $PQ 
eq QR 
eq PR$, $	riangle PQR$ is not isosceles.

Question

Solution