Question

The graph demonstrates a dilation with a scale factor of 1/2 for which of the following quadrilaterals?

a.
K(0, 8), L(4, 6), M(3, –3), N(–4, 8)
c.
K(4, 2), L(–4, 6), M(–6, –8), N(6, –10)
b.
K(–1, 0), L(–6, –3), M(–9, –2), N(–3, –9)
d.
K(1, 2), L(–3, 3), M(3, 5), N(2, 8)

Answer 1

Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.

In this exercise is given that a quadrilateral with vertices K'(2,1), L'(-2,3), M'(-3,-4) and N'(3,-5) was dilated by a scale factor of
`(1)/(2)`, and it is asked to find the vertices of the pre-image of the quadrilateral.

Image Pre-Image
K'(2,1) ---- (2×2,1×2) ---- K(4,2)
L'(-2,3) --- (-2×2,3×2) --- L(-4,6)
M'(-3,-4) -- (-3×2,-4×2) -- M(-6,-8)
N'(3,-5) --- (3×2,-5×2) --- N(6,-10)

The coordinates which represent the vertices of the quadrilateral's pre-image are K(4,2), L(-4,6), M(-6,-8), and N(6,-10) or in other words letter C from the given choices.