Calculate the total surface area of the triangular pyramid.
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Answer:
- scale factor is 2/3.
- coordinates of B are (9,-27).
- coordinates of C' are : (12,18)
Step-by-step explanation:
The image of a triangle after it has been dilated with a center at the origin has vertices at A’(-12,6) B’(6,-18) and C’ .
Point A has coordinates of (-18,9) and the pre- image of C' point C has coordinates of (18,12).
Clearly when we compare point A and point A' we see that the transformation is a dilation.
let the scale factor of dilation is 'k'.
i.e. A→ A'
i.e. k(-18,9)=(-12,6)
(-18k,9k)=(-12,6)
i.e. -18k=-12
and 9k=6
Hence, on solving we get:
k=2/3
i.e. the scale factor is 2/3.
Also,
we find the coordinates of B(c,d) by:
2/3(c,d)=(6,-18) since B→ B'
2/3×c=6
Hence c=9
and 2/3 ×d=-18
d=-27.
Hence, the coordinates of B are (9,-27).
Also the coordinates of C are (18,12)
Hence, coordinates of C' are:
Hence, the coordinates of C' are : (12,18)