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(i) Taking A as origin, find the coordinates of the vertices of the triangle.

(ii) What will be the coordinates of the vertices of triangle PQR if C is the origin?

Also calculate the areas of the triangles in these cases. What do you observe?

Answer :

(i) Taking A as origin, coordinates of the vertices P, Q and R are,

From figure:

P = (4, 6)

Q = (3, 2)

R = (6, 5)

Here AD is the x-axis and AB is the y-axis.

Area of triangle PQR in case of origin A:

Area of a triangle = \( \frac{1}{2} \ | \ [4(2 – 5) + 3 (5 – 6) + 6 (6 – 2)] \ | \ \)

\( = \ \frac{1}{2} \ | \ [– 12 – 3 + 24] \ | \ \)

\( = \ \frac{9}{2} \) sq. units

(ii) Taking C as origin, coordinates of vertices P, Q and R are,

From figure:

P = (12, 2)

Q = (13, 6)

R = (10, 3)

Here CB is the x-axis and CD is the y-axis.

Area of triangle PQR in case of origin C:

Area of a triangle = \( \frac{1}{2} \ | \ [ 12(6 – 3) + 13 ( 3 – 2) + 10( 2 – 6)] \ | \ \)

\( = \frac{1}{2} \ | \ [36 + 13 – 40] \ | \ \)

\( = \ \frac{9}{2} \) sq unit

This implies, Area of triangle PQR at origin A = Area of triangle PQR at origin C

Area is same in both case because triangle remains the same no matter which point is considered as origin.

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