ΔPQR has vertices P(5, –1), Q(0, 8), and R(7, 5). It is translated right 3 units and up 6 units. Find the coordinates of P', Q', and R'.
just add 3 to x and 6 to y in each coordinate pair
Okay, That makes sense, Thank you very much. ^_^
Well, well, well, it looks like ΔPQR has decided to go on a little adventure and take a hike! So, it's going to be a game of "Where in the World is ΔPQR?"
Alright, let's accompany ΔPQR on its journey. To translate it right 3 units, we have to tell it, "Hey, ΔPQR, take three steps to the right." And to top it off, we'll say, "And while you're at it, take 6 steps up!"
So, let's find the new coordinates of P'. P(5, -1) is going to take three steps to the right and end up at (5 + 3, -1) = (8, -1). P' is having a grand old time exploring the new coordinates!
Next up, we have Q(0, 8). This point likes to go with the flow, so it'll happily go three steps to the right and end up at (0 + 3, 8) = (3, 8). Q' is enjoying the view from its new location!
Lastly, we have R(7, 5). This point is feeling a bit adventurous, so it'll take three steps to the right and six steps up and end up at (7 + 3, 5 + 6) = (10, 11). R' is getting quite the workout with all that hiking!
So, after this little journey, the new coordinates of ΔPQR are P'(8, -1), Q'(3, 8), and R'(10, 11). Safe travels, ΔPQR!
To find the coordinates of the transformed points P', Q', and R', we need to apply the translation to each of the original coordinates as follows:
Let's start with P(5, -1):
1. Translate right 3 units: Add 3 to the x-coordinate.
New x-coordinate of P', x' = 5 + 3 = 8
2. Translate up 6 units: Add 6 to the y-coordinate.
New y-coordinate of P', y' = -1 + 6 = 5
So, P' has the coordinates (8, 5).
Now let's move on to Q(0, 8):
1. Translate right 3 units: Add 3 to the x-coordinate.
New x-coordinate of Q', x' = 0 + 3 = 3
2. Translate up 6 units: Add 6 to the y-coordinate.
New y-coordinate of Q', y' = 8 + 6 = 14
Therefore, Q' has the coordinates (3, 14).
Lastly, let's consider R(7, 5):
1. Translate right 3 units: Add 3 to the x-coordinate.
New x-coordinate of R', x' = 7 + 3 = 10
2. Translate up 6 units: Add 6 to the y-coordinate.
New y-coordinate of R', y' = 5 + 6 = 11
Thus, R' has the coordinates (10, 11).
To summarize:
P' has coordinates (8, 5)
Q' has coordinates (3, 14)
R' has coordinates (10, 11)
To find the coordinates of the vertices after the translation, we need to add the corresponding values for the translation to the original coordinates.
For the translation right 3 units, we add 3 to the x-coordinate of each point.
For the translation up 6 units, we add 6 to the y-coordinate of each point.
Coordinates of the original triangle ΔPQR:
P(5, –1)
Q(0, 8)
R(7, 5)
To find the coordinates of the translated points, we apply the translation:
Translation right 3 units:
P' = (Original x-coordinate of P + 3, Original y-coordinate of P)
= (5 + 3, -1)
= (8, -1)
Q' = (Original x-coordinate of Q + 3, Original y-coordinate of Q)
= (0 + 3, 8)
= (3, 8)
R' = (Original x-coordinate of R + 3, Original y-coordinate of R)
= (7 + 3, 5)
= (10, 5)
Therefore, the coordinates of the translated points are:
P' (8, -1)
Q' (3, 8)
R' (10, 5)