How to find the vertices of the image of #deltaPQR# having vertices #P(-1, 2), Q(-3, 5) & R(0, 4)# under the enlargement with scale factor -2 & centre at origin ?

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Answer 1 · 2018-06-11T11:10:23

#color(blue)(P'=(2,-4), Q'=(6,-10), R'=(0,-8)#

Since the centre of enlargement is at the origin, and the points #bbP#, #bbQ# and #bbR# can be looked upon as position vectors, we have:

#vec(OP)=((-1),(2))#

#vec(OQ)=((-3),(5))#

#vec(OR)=((0),(4))#

If we multiply each vector by the scale factor #-2#, this will give us the co-ordinates ( vertices ) of the image of #PQR#

#:.#

#-2vec(OP)=-2((-1),(2))=((2),(-4))#

#-2vec(OQ)=-2((-3),(5))=((6),(-10))#

#-2vec(OR)=-2((0),(4)) \ \ \ \ =((0),(-8))#

So the vertices of the image #PQR#:

#PQR'#

#P'=(2,-4), Q'=(6,-10), R'=(0,-8)#

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