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,y+3). This translation tells us that we should add 3 to the y-coordinates.
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(x,y) &→ & (x,y+3)
P(0,-4) &→ & P'(0,-1)
Q(1,3) &→ & Q'(1,6)
R(2,-5) &→ & R'(2,-2)
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-1,y+1). We need to subtract 1 from the x-coordinates and add 1 to the y-coordinates.
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(x,y) &→ &(x-1,y+1)
P'(0,-1) &→ & P''(-1,0)
Q'(1,6) &→ & Q''(0,7)
R'(2,-2) &→ & R''(1,-1)
Finally, we can use these new coordinates to draw the result of the composition, â–³P''Q''R''.
