Line AB contains ppint A(1,2) and point B(-2,-1) find the coordinates of A- and B' after a dilation with a scale factor of 5 with a center point of dilation at the origin
To find the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point at the origin, we can multiply each coordinate by the scale factor.
For point A(1,2):
x-coordinate of A' = 1 * 5 = 5
y-coordinate of A' = 2 * 5 = 10
Therefore, the coordinates of A' are (5,10).
For point B(-2,-1):
x-coordinate of B' = -2 * 5 = -10
y-coordinate of B' = -1 * 5 = -5
Therefore, the coordinates of B' are (-10,-5).
What's the answer bot
Apologies for the incorrect calculation in the previous response. Let's correct it:
To find the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point at the origin, we can multiply each coordinate by the scale factor.
For point A(1,2):
x-coordinate of A' = 1 * 5 = 5
y-coordinate of A' = 2 * 5 = 10
Therefore, the coordinates of A' are (5,10).
For point B(-2,-1):
x-coordinate of B' = -2 * 5 = -10
y-coordinate of B' = -1 * 5 = -5
Therefore, the coordinates of B' are (-10,-5).
So, the correct answer is:
The coordinates of A' are (5,10) and the coordinates of B' are (-10,-5).
Describe the dilation of triangle ABC with a scale factor of 5 and a center point of dilation at the origin (0,0)
The dilation of triangle ABC with a scale factor of 5 and a center point of dilation at the origin (0,0) means that each point of the triangle will be stretched or shrunk by a factor of 5 from the origin.
Let's denote the vertices of triangle ABC as A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃). After the dilation, the new coordinates, A', B', and C', can be found as:
A'(5x₁, 5y₁)
B'(5x₂, 5y₂)
C'(5x₃, 5y₃)
This means that each x-coordinate and y-coordinate of the original triangle is multiplied by the scale factor 5 to obtain the corresponding coordinate of the dilated triangle.
In essence, the dilation enlarges or reduces the size of each side of the triangle by a factor of 5, while maintaining the same shape and relative angles.
What's the answer
To describe the dilation of triangle ABC with a scale factor of 5 and a center point of dilation at the origin (0,0):
Triangle ABC has three vertices: A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃).
After the dilation, the coordinates of the new vertices A', B', and C' are:
A'(5x₁, 5y₁)
B'(5x₂, 5y₂)
C'(5x₃, 5y₃)
Each coordinate (x, y) of the original triangle is multiplied by the scale factor 5 to determine the corresponding coordinate of the dilated triangle.
Therefore, the triangle is enlarged or reduced in size by a factor of 5 with respect to the origin (0,0) as the center of dilation, while maintaining the same shape and relative angles.