Polygon xyzw is dilated by a scale factor of 2 with point t as the center of dilation, resulting in the image x′y′z′w′. if point t lies on `bar(yz)`, what can be said about `bar(y'z')` ? a. `bar(y'z')` passes through point t but has a different slope than `bar(yz)`. b. `bar(y'z')` passes through point t and has the same slope as `bar(yz)` . c. `bar(y'z')` does not pass through point t but has the same slope as `bar(yz)`. d. `bar(y'z')` does not pass through point t and has a different slope than `bar(yz)`.

B.

`bar(Y'Z')` passes through point T and has the same slope as `bar(YZ)`

Explanation:

Let us understand what is dilation first.

A dilation is one type of  transformation of a two-dimensional geometric figure that transforms a shape into  an image, which is similar in form to the initial object but varies in size. The scale factor determines the degree or amount to which the object is increased or decreased. The origin of a coordinate plane with the points x = 0 and y = 0 is the most common center of dilation in geometry, but here we are given a point T on YZ

Since dilation does not change the shape but gives a similar image it follows that the centre of dilation T will still remain on the same bar Y'Z' enlarged part of YZ.  Also slope would remain the same as the transformed figure would be similar to the original.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

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step-by-step explanation: