A right triangle has vertices

MATHEMATICS · Multi-part · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

P(2,3)

Q(5,3)

and

R(2,7)

. (i) Plot

\triangle PQR

on the Cartesian plane and name the right angle. (ii) Reflect each vertex of the triangle in the

y

-axis to obtain the images

P'

Q'

and

R'

. Write the coordinates of

P'

Q'

and

R'

. (iii) Draw

\triangle P'Q'R'

and shade the combined figure

\triangle PQR \cup \triangle P'Q'R'

. (iv) Show that the combined figure is symmetrical about the

y

-axis, citing coordinate pairs to support your explanation. (v) Find the total area of the shaded figure.