Question

The points A (2, 3), B (4, 5) and C (7, 2) are the vertices of ∆ABC.
(i) Write down the co-ordinates of $A_1,B_1,C_1$if $\Delta A_1{B}_1{C}_1$ is the image of ∆ ABC when reflected in the origin.
(ii) Write down the co-ordinates of $A_2,B_2,C_2$ if $\Delta A_2{B}_2{C}_2$ is the image of ∆ ABC when reflected in the x-axis.
(iii) Assign the special name to the quadrilateral $BC{C}_2{B}_2$ and find its area.

Answer 1

Given, points A (2, 3), B (4, 5) and C (7, 2) are the vertices of ∆ ABC.

And $A_1,B_1$ and $C_1$ are the images of A, B and C reflected in the origin.

(i) Hence,

Co-ordinates of $A_1$ = (-2, -3)

Co-ordinates of $B_1$ (-4, -5) and

Co-ordinates of $C_1$ (-7, -2).

(ii) Now,

Co-ordinates of $A_2,B_2$ and $C_2$ the images of A, B and C when reflected in x-axis are:

$A_2$ (2, – 3), $B_2$ (4, – 5), $C_2$ (7, – 2)

(iii) The quadrilateral formed by joining the points, $BC{C}_2{B}_2$ is an isosceles trapezium and its area is

$=½(B{B}_2+C{C}_2)\times 3$

= ½ (10 + 4) x 3

= ½ x 14 x 3

= 21 sq. units