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Standard XII

Mathematics

Ratios of Distances between Centroid, Circumcenter, Incenter and Orthocenter of Triangle

Describe full...

Question

Describe fully the single transformation that maps triangle $A$ onto triangle $B$ .

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Solution

Here the triangle $A$ is translation to the triangle $B$ .
The ratio of $x$ -coordinates is $\frac{7}{4} = 1.75$ , so the scale factor of the dilation that maps $(4, 6)$ onto $(7, 9)$ is $1.75$ .
So, translation: $(x, y)$ $\mapsto$ $(x - 2, y - 1)$

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The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A" B" C".

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Describe fully the single transformation that maps triangle A onto triangle B.

Here the triangle A is translation to the triangle B.The ratio of x-coordinates is 74=1.75, so the scale factor of the dilation that maps (4,6) onto (7,9) is 1.75.So, translation: (x,y) ↦ (x−2,y−1)

Describe fully the single transformation that maps triangle $A$ onto triangle $B$ .

Here the triangle $A$ is translation to the triangle $B$ .
The ratio of $x$ -coordinates is $\frac{7}{4} = 1.75$ , so the scale factor of the dilation that maps $(4, 6)$ onto $(7, 9)$ is $1.75$ .
So, translation: $(x, y)$ $\mapsto$ $(x - 2, y - 1)$