Triangle ABC has vertices point A 2,1, point B 4,3 and point C -2, 5. Find the coordinates of A, B and C after the dialation with a scale factor of 7 and a center point of dialation at the origin 0,0
To find the coordinates of A, B, and C after dilation with a scale factor of 7 and a center point of dilation at the origin (0,0), multiply the x and y coordinates of each point by the scale factor.
For point A (2,1):
New x-coordinate of A = 2 * 7 = 14
New y-coordinate of A = 1 * 7 = 7
So, the new coordinates of A after dilation are (14, 7).
For point B (4,3):
New x-coordinate of B = 4 * 7 = 28
New y-coordinate of B = 3 * 7 = 21
So, the new coordinates of B after dilation are (28, 21).
For point C (-2,5):
New x-coordinate of C = -2 * 7 = -14
New y-coordinate of C = 5 * 7 = 35
So, the new coordinates of C after dilation are (-14, 35).
Therefore, the coordinates of A, B, and C after dilation with a scale factor of 7 and a center point of dilation at the origin (0,0) are:
A: (14, 7)
B: (28, 21)
C: (-14, 35)
Triangle ABC has vertices point A 2,1, point B -2, 2 and point C -3, -1. After dialation triangle A,'B' C' has vertices point A' 4, 2, point B' -2, 2 and point C' -6, -2. Determine the scale factor for the dialation of triangle ABC with a center point of dialation at the origin 0,0
To find the scale factor of the dilation, we need to calculate the ratio of the corresponding side lengths.
Let's consider the distance between point A and the origin, which is the center point of dilation.
Original distance of point A from the origin, OA: √((2-0)^2 + (1-0)^2) = √(4+1) = √5
New distance of point A' from the origin, O'A': √((4-0)^2 + (2-0)^2) = √(16+4) = √20
The scale factor, k, is given by the ratio of the new distance to the original distance:
k = O'A' / OA = √20 / √5 = √(20/5) = √4 = 2
Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0,0) is 2.