Jimmy wants to serve iced tea at his birthday party. He purchases 14 containers filled with 1.5 liters of tea. Approximately how
1 answer:
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Answer: The scale factor of the dilation is 0.5.
Explanation:
It is given that ABCD is polygon which is reflected and dilated , then we get PQRS.
The vertices of ABCD are (2, 2), (6, 8), (12, 8), and (16, 2) respectively. The vertices of image PQRS are (11, 15),(9, 12), (6, 12), and (4, 15) respectively.
The reflection affects the coordinates but does not affect the length of the sides.
But when we talk about dilation it affects the length of sides according to the scale factor or a constant factor.
If a line segment AB is dilated by scale factor k then length of A'B' is k times length of AB.
.... (1)
So we have to find any side length of preimage and the side length of that side in image. it means we have to find AB and PQ.
Use distance formula to find the side length.
It is noticed that the size of side in preimage is and the size of same side in image is
.
Using equation (1), we get
Hence, the value of scale factor is 0.5.
With even just two points, you can find the equation of a line in slope-intercept form.
Slope-intercept form: where
is the slope and
is the y-intercept
<u>1) Solve for the slope (</u><u>)</u>
The equation to solve for the slope is when the two points are
and
. Plug the coordinates of these points into the equation and solve for
.
Then, plug into
.
<u>1) Solve for the y-intercept (</u><u>)</u>
Then, take any of the given points and plug it into along with the slope. Isolate
to get the y-intercept. Then, plug both m and b back into
to get your final equation.
I hope this helps!