In which quadrant would the image of point (5,-3) fall after a dilation using a factor of -3?
Under a dilation of -3, the point (5,-3) would be
(-15,9)
Where is that point located?
quadrant 4
In which quadrant would the image of point (-5,3) fall after a dilation using a factor of 3? *
Well, if we're talking about a dilation by a factor of -3, it's like multiplying the coordinates of the point by -3. So, if we take the point (5, -3) and multiply its coordinates by -3, we get (-15, 9).
Now, let's see where this transformed point falls. Hmm... (-15, 9) definitely doesn't fall into any quadrant since it's not on any of the axes. I guess you could say it's in the "quadrant of confusion"!
To determine the image of a point after a dilation, we need to multiply the coordinates of the point by the dilation factor.
In this case, the dilation factor is -3. When the dilation factor is negative, the image will be reflected across the origin.
Let's multiply the coordinates of the point (5, -3) by the dilation factor:
Image x-coordinate = 5 * (-3) = -15
Image y-coordinate = -3 * (-3) = 9
So, the image of the point (5, -3) after a dilation with a factor of -3 would be (-15, 9).
Now, let's determine the quadrant where this image falls.
The image has negative x-coordinate (-15) and positive y-coordinate (9).
Using the quadrant system, where quadrant I is top-right, quadrant II is top-left, quadrant III is bottom-left, and quadrant IV is bottom-right, we can see that the image falls into the second quadrant.
Therefore, the image of the point (5, -3) would fall into quadrant II after the dilation with a factor of -3.