Calculate the new points by adding or subtracting the translations of the x- and y-coordinates.
Practice makes perfect
We are given three vertices of â–ł PQR. To graph the triangle, let's plot the points and then connect them.
Next, we can do the first of the given translations, (x,y) → (x+1,y+2). This translation tells us that we should add 1 to the x-coordinates and 2 to the y-coordinates.
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(x,y) &→ & (x+1,y+2)
P(0,-4) &→ & P'(1,-2)
Q(1,3) &→ & Q'(2,5)
R(2,-5) &→ & R'(3,-3)
Let's add these new vertices to the same coordinate plane.
Now we can translate the new image, △ P'Q'R', using the second of the given translations, (x,y) → (x-4,y+1). We need to subtract 4 from the x-coordinates and add 1 to the y-coordinates.
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(x,y) &→ &(x-4,y+1)
P'(1,-2) &→ & P''(-3,-1)
Q'(2,5) &→ & Q''(-2,6)
R'(3,-3) &→ & R''(-1,-2)
Finally, we can use these new coordinates to draw the result of the composition: â–łP''Q''R''.
