A point is translated on the coordinate plane from (4,-1) to (4,2). Journey writes the function g(y)=y+k to describe the translation. What is the value of k?
To find the value of k, we can compare the y-coordinates of the original point and the translated point. The original y-coordinate is -1 and the translated y-coordinate is 2.
We can subtract the original y-coordinate from the translated y-coordinate:
2 - (-1) = 2 + 1 = 3
So, k = 3.
To find the value of k, we need to determine the vertical translation that occurred in the transformation.
In this case, the y-coordinate of the point changed from -1 to 2. The change in y-coordinate is given by:
Change in y = new y-coordinate - old y-coordinate
= 2 - (-1)
= 2 + 1
= 3
We know that the function g(y) represents the vertical translation, and it is given by g(y) = y + k. Here, y represents the old y-coordinate, and k is the vertical translation.
Since the change in y-coordinate is equal to the vertical translation (k), we can conclude that:
k = 3
So, the value of k is 3.
To find the value of k in the function g(y) = y + k that describes the translation of a point from (4,-1) to (4,2), we will use the concept of translation on the coordinate plane.
In a translation, the x-coordinate remains the same, while the y-coordinate changes. In this case, the x-coordinate remains as 4 since there is no horizontal movement involved. However, the y-coordinate changes from -1 to 2, indicating an upward movement by 3 units.
Since k represents the change in the y-coordinate, we can determine its value by subtracting the original y-coordinate from the new y-coordinate.
k = new y-coordinate - original y-coordinate
= 2 - (-1)
= 2 + 1
= 3
Therefore, the value of k is 3. In the function g(y) = y + k, the value of k is 3, so the translation brings the point up by 3 units.