Asequence of transformations maps ∆abc to ∆a′b′c′. the sequence of transformations that maps ∆abc to ∆a′b′c′ is a reflection across the ( 1. y-axis 2. x-axis 3. line y=x 4.
line y=-x) followed by a translation (1. 4 units to the right and 10 units up 2. 8 units to the right and 4 units up 3. 10 units to the right and 2 units up 3. 10 units to the right and 4 units up)

Step-by-step explanation:

In the attached diagram, the green polygon A"B"C" is the reflection of ABC across the line y=x. Then the purple polygon A'B'C' is the translation of A"B"C" 10 units to the right and 4 units up.

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You can tell a reflection is involved, because the clockwise order of A, B, C in the original is reversed to counterclockwise in A'B'C'. The left-right horizontal line AC becomes the down-up vertical line A'C', so you know the reflection is across the line y=x, and not the line y=-x.

After the reflection, point A" is located at (2, -6), so moving it to A'(12, -2) entails a translation 10 units right and 4 units up.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

this is false ^.^ lol