Write the coordinates of the image of the pont (-3,9) on the graph y=x^2 when each of the following transformations are applied:
a) a reflection in the x-axis followed by a vertical translation 4 units up
b) a vertical stretch by a factor of 1/3 about the x-axis
reflection: (x,y) -> (x,-y)
up 4: (x,y) -> (x,y+4)
so, (-3,9) -> (-3,-9) -> (-3,-5)
usually stretches are termed in the x- or y- direction
"about the x-axis?" Hmmm
If you mean stretched toward the x-axis (that is, in the y-direction), then (x,y) -> (x,y/3)
If you mean stretched along the x-axis (in the x-direction), then (x,y) -> (x/3,y)
Pick one, and plug in your numbers.
a) To find the coordinates of the image of the point (-3, 9) when a reflection in the x-axis is applied, we flip the y-coordinate while keeping the x-coordinate the same. So, the new point after the reflection is (-3, -9).
Next, we apply a vertical translation 4 units up. This means we add 4 to the y-coordinate. Thus, the new point after the translation is (-3, -5).
b) To find the coordinates of the image of the point (-3, 9) when a vertical stretch by a factor of 1/3 about the x-axis is applied, we multiply the y-coordinate by 1/3 while keeping the x-coordinate the same. So, the new point after the vertical stretch is (-3, 9/3) or (-3, 3).
To find the coordinates of the image of the point (-3,9) after each of the given transformations, we can follow these steps:
a) Reflection in the x-axis followed by a vertical translation 4 units up:
1. Reflection in the x-axis: To reflect a point in the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate. Thus, the image of (-3,9) after reflection in the x-axis is (-3,-9).
2. Vertical translation 4 units up: To perform a vertical translation, we add the specified amount to the y-coordinate. So, adding 4 to the y-coordinate of the image (-3,-9) gives (-3,-5).
Therefore, the image of the point (-3,9) after the given transformations is (-3,-5).
b) Vertical stretch by a factor of 1/3 about the x-axis:
1. Vertical stretch by a factor of 1/3: To stretch the graph vertically by a factor of 1/3, we multiply the y-coordinate by 1/3. Applying this transformation to the image obtained in part a), we get (-3, -5) * (1/3) = (-3, -5/3).
So, after the vertical stretch by a factor of 1/3 about the x-axis, the coordinates of the image of the point (-3,9) are (-3, -5/3).