Suppose for the moment that the inequality holds for all :
Expanding everything gives
In particular, the inequality says that for any choice of
. But if
and
, then
while
.
So one possible choice of could be
and
. Then we get
but clearly it's not true that .
Answer:
Yes! The equation, y = 12x + 28 , work.
Step-by-step explanation:
The line passes through points (-1, 16) and (5, 88)
The slope of the line = change in y ÷ change in x
i.e slope = = 12
Taking another point (x ,y) on the line;
Slope is = 12
y - 16 = 12x + 12
y = 12x + 12 + 16
y = 12x + 28
So the equation, y = 12x + 28, work!
A dilated shape will either be enlarged or compressed.
<em>Allen did not make any mistake, and the scale factor is 3.</em>
The dimension of the smaller rectangle (figure Z) is:
3 units by 4 units
The corresponding dimension of the bigger rectangle (figure Z') is:
9 units by 12 units
The scale factor (k) is calculated by dividing the dimensions of Z' by Z.
So, we have:
or
Notice that both values of k are the same (i.e. 3)
This means that the scale factor is 3
Also figure Z and Z' share the same center of origin at point X
This means that the center of dilation from Z to Z' is X
Hence,
Allen made no mistake, and she is correct about the scale factor.
Read more about dilations at: