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

(i) Write down the coordinates of A1, B1, C1 if △A1B1C1 is the image of △ABC when reflected in the origin.

(ii) Write down the coordinates of A2, B2, C2 if △A2B2C2 is the image of △ABC when reflected in the x-axis.

(iii) Assign the special name to quadrilateral BCC2B2 and find its area.

Reflection

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Answer

The graph is shown below:

The points A(2, 3), B(4, 5) and C(7, 2) are the vertices of △ABC. (i) Write down the coordinates of A1, B1, C1 if △A1B1C1 is the image of △ABC when reflected in the origin. (ii) Write down the coordinates of A2, B2, C2 if △A2B2C2 is the image of △ABC when reflected in the x-axis. (iii) Assign the special name to quadrilateral BCC2B2 and find its area. Reflection, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

(i) From graph we get,

The coordinates of A1, B1, C1 are (-2, -3), (-4, -5) and (-7, -2) respectively.

(ii) From graph we get,

The coordinates of A2, B2, C2 are (2, -3), (4, -5) and (7, -2) respectively.

(iii) From graph we get,

BCC2B2 formed is an isosceles trapezium.

We know that,

Area of trapezium = 12×\dfrac{1}{2} \times sum of parallel sides ×\times distance between them

=12×(BB2+CC2)×3=12×(10+4)×3=12×42=21 sq. units= \dfrac{1}{2} \times (\text{BB}2 + \text{CC}2) \times 3 \\[1em] = \dfrac{1}{2} \times (10 + 4) \times 3 \\[1em] = \dfrac{1}{2} \times 42 \\[1em] = 21 \text{ sq. units}

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