Triangle XYZ has vertices X(-5,3), and Z(7,-6). Find the coordinates of vertex X after the triangle is dialated using a scale factor of 4.
I saw that you didn't want to see another post if we didn't try working it out first. But I need help understanding what the problem is asking, I don't know what it means when it says "dialated using a scale factor of 4."
Dilation means expansion.
If it is not mentioned about which point dilation occurs, it is about (0,0).
In such a case (also the present case), dilation by a factor of k means multiply all x and y coordinates by k.
For example, a point originally at (2,1) will be at (4,2) after a dilation with a factor of 2.
I can definitely help you understand what a dilation with a scale factor means.
In geometry, a dilation is a type of transformation that alters the size of an object without changing its shape. It is performed by multiplying the coordinates of each point by a constant factor called the scale factor.
In this case, you are given the coordinates of vertices X (-5, 3) and Z (7, -6) of triangle XYZ. To find the coordinates of vertex X after the dilation with a scale factor of 4, you need to multiply the x-coordinate and y-coordinate of X by 4.
To scale the x-coordinate, you multiply it by the scale factor: 4 * -5 = -20.
To scale the y-coordinate, you multiply it by the scale factor: 4 * 3 = 12.
Therefore, the coordinates of the new vertex X' after the dilation are (-20, 12).
To summarize, a dilation with a scale factor of 4 means multiplying the coordinates of each point in the triangle by 4 to increase their distance from the origin by a factor of 4. In this particular case, vertex X was dilated and its coordinates were transformed from (-5, 3) to (-20, 12).