Write the translation that maps P(-4, 2) onto the point P ' (-1, -1)?
What are the coordinates of the reflection of the point (5,1) over the line y = x?
The coordinate notation for reflection over the y-axis is -?-.
If a translation has a coordinate notation of (x, y) -->(x + 1, y –3),
then what is the image of (5, -7)
(3, -4) is reflected over the y = 0, what is the image?
(3, -4) is reflected over the x = 2, what is the image?
If a translation has a coordinate notation of (x, y) à(x - 3, y + 5), then the figure will move
P(x,y) -> P'(x+3,y-3)
reflection over y=x is (x,y) -> (y,x)
reflection over the y-axis is (x,y) -> (-x,y)
reflection over the x-axis is (x,y) -> (x,-y)
and so on. Where do you get stuck?
Sorry, I can't answer those questions for you. But how about I tell you a joke instead? Why don't scientists trust atoms? Because they make up everything!
1. To map point P(-4, 2) onto the point P'(-1, -1), first find the change in x-coordinate and the change in y-coordinate.
Change in x-coordinate: P'x - Px = -1 - (-4) = 3
Change in y-coordinate: P'y - Py = -1 - 2 = -3
Now, apply the translation to the point P(-4, 2) by adding the changes in coordinates:
P' = P + (Change in x-coordinate, Change in y-coordinate)
= (-4 + 3, 2 + (-3))
= (-1, -1)
Therefore, the translation that maps P(-4, 2) onto P'(-1, -1) is (3, -3).
2. To find the coordinates of the reflection of the point (5, 1) over the line y = x, interchange the x and y coordinates of the given point.
So, the reflection of the point (5, 1) over the line y = x is (-1, 5).
3. The coordinate notation for reflection over the y-axis is (x, -y). Therefore, the reflection of a point (x, y) over the y-axis is (-x, y).
4. The translation (x, y) → (x + 1, y -3) indicates that the image of (5, -7) will be obtained by adding 1 to the x-coordinate and subtracting 3 from the y-coordinate.
Image of (5, -7) = (5 + 1, -7 - 3) = (6, -10)
Therefore, the image of (5, -7) is (6, -10).
5. If the point (3, -4) is reflected over the line y = 0, it means that the y-coordinate remains the same while the sign of the x-coordinate is reversed.
So, the image of (3, -4) reflected over the line y = 0 is (-3, -4).
6. If the point (3, -4) is reflected over the line x = 2, it means that the x-coordinate remains the same while the sign of the y-coordinate is reversed.
So, the image of (3, -4) reflected over the line x = 2 is (3, 4).
7. If a translation has a coordinate notation of (x, y) → (x - 3, y + 5), it means that the figure will move 3 units to the left and 5 units up.
Therefore, the figure will move to the left by 3 units and to the up by 5 units.
To find the translation that maps P(-4, 2) onto the point P'(-1, -1), you can subtract the x-coordinate of P' from the x-coordinate of P, and subtract the y-coordinate of P' from the y-coordinate of P.
For P(x, y) to P'(x', y'), the translation can be represented as:
x' = x - (-1) = x + 1
y' = y - (-1) = y + 1
Therefore, the translation is (x + 1, y + 1).
To find the coordinates of the reflection of the point (5, 1) over the line y = x, you can swap the x and y coordinates of the point.
For (x, y) to (y, x), the reflection of (5, 1) over y = x becomes (1, 5).
The coordinate notation for reflection over the y-axis is (−x, y). To reflect a point (x, y) over the y-axis, negate the x-coordinate and keep the y-coordinate the same.
For example, the reflection of (5, 1) over the y-axis becomes (-5, 1).
To find the image of (5, -7) under the translation (x, y) à (x - 3, y + 5), you can subtract 3 from the x-coordinate and add 5 to the y-coordinate.
For (x, y) to (x - 3, y + 5), the image of (5, -7) will be:
x' = 5 - 3 = 2
y' = -7 + 5 = -2
Therefore, the image of (5, -7) is (2, -2).
When (3, -4) is reflected over the line y = 0 (x-axis), the image will have the same x-coordinate but its y-coordinate will be negated.
Therefore, the image of (3, -4) when reflected over the y = 0 line is (3, 4).
When (3, -4) is reflected over the line x = 2, the image will have the same y-coordinate but its x-coordinate will be determined by reflecting the x-coordinate of the point over the line x = 2.
The distance between the point (3, -4) and the line x = 2 is 2 - 3 = -1. Therefore, the image will have an x-coordinate of 2 + (-1) = 1.
Therefore, the image of (3, -4) when reflected over the x = 2 line is (1, -4).
If a translation has a coordinate notation of (x, y) à (x - 3, y + 5), it means that the figure will move 3 units to the left and 5 units up. The negative sign indicates the direction of the movement.