CBSE Class 10-Mathematics: Chapter – 7 Coordinate Geometry Part 24 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 19:

The class X students of a secondary school in Krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmoharare 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 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 if C is the origin? Also calculate the area of the triangle in these cases. What do you observe?

The Area of the Triangle

Answer:

(i) Taking A as the origin, AD and AB as the coordinate axes. Clearly, the points P, Q and

respectively.

(ii) Taking C as the origin, CB, and CD as the coordinate axes. Clearly, the points and are given by and respectively.

We know that the area of the triangle

And Area of (Second case)

Hence, the areas are same in both the cases.

Question 20:

ABCD is a rectangle formed by joining points A . P, Q, R and S are the mid-points of AB, BC, CD and DA, respectively. Is the quadrilateral PQRS a square? Or a rhombus? Justify your answer.

Answer:

Using distance formula,

Now,

And

Since all the sides are equal but the diagonals are not equal.

is a .