Draw figures with the given vertices in a coordinate plane. Which figures are similar? Explain your reasoning.
Triangle $A : (- 4, 4), (- 2, 4), (- 2, 0)$
Triangle $B : (- 2, 2), (- 1, 2), (- 1, 0)$
Triangle $C : (6, 6), (3, 6), (3, 0)$

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Solution

Plot the graph for all triangles.
For triangle $A : (- 4, 4), (- 2, 4), (- 2, 0)$
For triangle $B : (- 2, 2), (- 1, 2), (- 1, 0)$
For triangle $C : (6, 6), (3, 6), (3, 0)$
Hence, all figures are similar.

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Question 4(c) :

Look at the figures and write ‘<’ or ‘>’ between the given pairs of fractions:

$\frac{2}{3} □ \frac{2}{4}$

I. The centroid of the triangle formed by $(2, 3, - 1), (5, 6, 3), (2, - 3, 1)$ is	a) $(2, 2, 2)$
II. The circumcentre of the triangle formed by $(1, 2, 3), (2, 3, 1), (3, 1, 2)$ is	b) $(3, 1, 4)$
III. The orthocenter of the triangle formed by $(2, 1, 5), (3, 2, 3), (4, 0, 4)$ is	c) $(1, 1, 0)$
IV. The incentre of the triangle formed by $(0, 0, 0), (3, 0, 0), (0, 4, 0)$ is	d) $(3, 2, 1)$
	e) $(0, 0, 0)$

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