A point (-5, 4) is mapped onto (-1, -1) by a translation. Find the image of (-4, 5) under the same translation.
this all
well first the amount of translation when (-5,4) is moved to (-1,-1) what amount of translation is this in terms of x-axis? Answer to that is it moved 4 points or units towards right on x-axis.
In terms of y-axis it moved from 4 to -1 so it moved 5 points down. So in very simple way, it can be said the translation is 4 right, 5 down.
So the image of point (-4,5) after it is moved 4 right and 5 down would be point (0,0) because you do (-4,5) will be translated to (-4+4, 5-5).
Are you give an equation for this or is that all you are given?
To go from -5 to -1, we moved 4 to the right
to go from 4 to -1, we moved 5 to the left, so
(x,y) ---> (x+4, y-5)
then (-4,5) ---> (0,0)
To find the image of a point under a translation, we need to determine the amount and direction of the translation and apply it to the coordinates of the given point.
In this case, we are given that the point (-5, 4) is mapped onto (-1, -1) by a translation. To determine the translation, we subtract the coordinates of the original point from the coordinates of its image.
The translation vector is calculated as follows:
Translation vector = (x2 - x1, y2 - y1)
= (-1 - (-5), -1 - 4)
= (4, -5)
Now that we have the translation vector, we can apply it to the coordinates of the point (-4, 5) to find its image.
New coordinates = (x + Δx, y + Δy)
= (-4 + 4, 5 - 5)
= (0, 0)
Therefore, the image of the point (-4, 5) under the same translation is (0, 0).