Triangle ABC has a vertices point A(-2,-2), point B(-4,-3), and point C after a dilation with a scale factor of 3 and a scale factor of 3 and a center point of dilation at the origin.
To find the coordinates of the vertices of the dilated triangle, we need to multiply the coordinates of each original vertex by the scale factor. Since the center of dilation is at the origin (0,0), the coordinates of the dilated vertices are:
Vertex A:
x-coordinate: -2 * 3 = -6
y-coordinate: -2 * 3 = -6
Dilated coordinates: A(-6, -6)
Vertex B:
x-coordinate: -4 * 3 = -12
y-coordinate: -3 * 3 = -9
Dilated coordinates: B(-12, -9)
Vertex C:
Since the center of dilation is the origin, point C remains the same.
Dilated coordinates: C(-2, -2)
Therefore, the vertices of the dilated triangle ABC with a scale factor of 3 and a center point of dilation at the origin are A'(-6, -6), B'(-12, -9), and C'(-2, -2).
To find the coordinates of point C after a dilation with a scale factor of 3 and a center point of dilation at the origin, we can use the following formula:
P' = P * r
where P' is the coordinates of the point after dilation, P is the original coordinates of the point, and r is the scale factor.
Let's first calculate the coordinates of point C after a dilation with a scale factor of 3:
Original coordinates of point C: (x, y)
Scaled coordinates of point C: (3x, 3y)
Since the center of dilation is at the origin, the coordinates of point C after dilation become (3x, 3y).
Now, let's substitute the original coordinates of point C into the formula:
Original coordinates of point C: (x, y)
Scaled coordinates of point C: (3x, 3y)
So, the coordinates of point C after dilation with a scale factor of 3 and a center point at the origin are (3 * -2, 3 * -2) = (-6, -6).
To find the new vertices of triangle ABC after a dilation with a scale factor of 3 and a center point of dilation at the origin, you can multiply the coordinates of each point by the scale factor.
Let's start with the original coordinates of the triangle:
Point A: (-2, -2)
Point B: (-4, -3)
Point C: (x-coordinate, y-coordinate) - We need to find the coordinates of point C.
To find the new coordinates of point A', we can use the formula:
A' = (sx, sy)
where sx and sy are the scaled coordinates of point A.
For point A:
scaled x-coordinate of A = (-2) * 3 = -6
scaled y-coordinate of A = (-2) * 3 = -6
So, the new coordinates of point A' (after dilation) are A'(-6, -6).
Similarly, for point B:
scaled x-coordinate of B = (-4) * 3 = -12
scaled y-coordinate of B = (-3) * 3 = -9
So, the new coordinates of point B' (after dilation) are B'(-12, -9).
Now, to find the new coordinates of point C', we need to apply the same scaling to point C, but since its coordinates are not provided, we cannot determine the exact coordinates of point C'.
However, using the given information, we know that the center of dilation is at the origin (0, 0). Since point C lies on the line segment joining the origin and the original position of point C, we can say that the new position of point C' after dilation is in the same direction as the original position of point C, but three times farther from the origin.
Hence, we can conclude that the new coordinates of point C' after dilation are three times the original coordinates of point C.
Therefore, the new coordinates of point C' are (3 * x-coordinate, 3 * y-coordinate).