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Write a translation rule that maps point
D (7,−3) onto point D'(2,5).
Can someone help me
7-5 = 2
-3+8 = 5
so (x,y)→(x-5,y+8)
Sure, I'll help you! Don't worry, I'm fluent in clown language, so I'll make it fun.
To find the translation rule, we need to look at how the x-coordinate and y-coordinate change from point D to point D'.
To make it easier for us to visualize, let's see D and D' as two clown emoji friends. 🤡🤡
Now, our clown friend D is located at a circus tent, specifically at the coordinates (7, -3). But our friend D' is feeling a bit adventurous and wants to explore a different part of the circus. They end up at the coordinates (2, 5).
To map point D onto point D', we need to figure out how our clown friend D got from (7, -3) to (2, 5).
To move from (7, -3) to (2, 5), our clown friend had to go left by 5 units (7 - 2 = 5) and up by 8 units (-3 + 8 = 5).
So the translation rule is:
x-coordinate: Move 5 units to the left
y-coordinate: Move 8 units up
Or, in clown language:
D(7, -3) 🤡 🤡 D'(2, 5)
To move from D to D', our clown friend has to go "left by 5 units, and rise up by 8 units."
I hope that helps, and remember, never take life too seriously, especially when dealing with clowns! 🎪🤡
To write a translation rule that maps point D(7,-3) onto point D'(2,5), you can follow these steps:
1. Determine the horizontal shift: Subtract the x-coordinate of point D' from the x-coordinate of point D.
Horizontal shift = x-coordinate of D - x-coordinate of D'
Horizontal shift = 7 - 2 = 5
2. Determine the vertical shift: Subtract the y-coordinate of point D' from the y-coordinate of point D.
Vertical shift = y-coordinate of D - y-coordinate of D'
Vertical shift = -3 - 5 = -8
3. Write the translation rule using the horizontal and vertical shifts:
(x, y) --> (x + horizontal shift, y + vertical shift)
Therefore, the translation rule that maps point D(7,-3) onto point D'(2,5) is:
(x, y) --> (x + 5, y - 8)
Thus, to map any other point using this translation rule, you would add 5 to the x-coordinate and subtract 8 from the y-coordinate.
To write the translation rule that maps point D(7, -3) onto point D'(2, 5), we need to determine how the x and y coordinates of D are translated to the x and y coordinates of D'.
A translation is a type of transformation that moves a point a certain distance in a certain direction. In this case, we want to move point D(7, -3) to point D'(2, 5).
To determine the translation rule, we need to calculate the horizontal and vertical distances between the two points.
Horizontal distance (x-axis):
To calculate the horizontal distance, subtract the x-coordinate of D' from the x-coordinate of D:
Δx = x-coordinate of D' - x-coordinate of D
Δx = 2 - 7 = -5
Vertical distance (y-axis):
To calculate the vertical distance, subtract the y-coordinate of D' from the y-coordinate of D:
Δy = y-coordinate of D' - y-coordinate of D
Δy = 5 - (-3) = 8
The translation rule for this transformation is: (x, y) → (x - Δx, y - Δy).
For point D (7, -3), applying the translation rule, we have:
D → D'
(7, -3) → (7 - (-5), -3 - 8)
(7, -3) → (7 + 5, -3 + 8)
(7, -3) → (12, 5)
So, the translation rule that maps point D (7, -3) onto point D' (2, 5) is: (x, y) → (x - 5, y + 8).