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–³ 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–³P''Q''R''.
