A(-3,4), B(2,-4)
A'(-6,8), B'(4,-8)
Determine the scale factor used in the dilation of AB, with a center point of dilation at the origin.
The scale factor is __
Apologies for the mistake. Let's find the correct scale factor used in the dilation of AB.
The distance between points A and B can be calculated using the distance formula:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
AB = sqrt((2 - (-3))^2 + (-4 - 4)^2)
= sqrt(5^2 + (-8)^2)
= sqrt(25 + 64)
= sqrt(89)
The distance between the corresponding points A' and B' can also be calculated using the distance formula:
A'B' = sqrt((x2' - x1')^2 + (y2' - y1')^2)
A'B' = sqrt((4 - (-6))^2 + (-8 - 8)^2)
= sqrt(10^2 + (-16)^2)
= sqrt(100 + 256)
= sqrt(356)
The scale factor is the ratio of A'B' to AB:
scale factor = A'B' / AB
= sqrt(356) / sqrt(89)
= sqrt(4 * 89) / sqrt(89)
= sqrt(4) * sqrt(89) / sqrt(89)
= 2 * sqrt(89) / sqrt(89)
= 2
Therefore, the scale factor used in the dilation of AB, with a center point of dilation at the origin, is 2.
To find the coordinates of the image points after a dilation with a scale factor of 7 and a center point of dilation at the origin, we can multiply the coordinates of each point by the scale factor.
Let's find the coordinates of A':
x-coordinate of A' = 7 * x-coordinate of A = 7 * 2 = 14
y-coordinate of A' = 7 * y-coordinate of A = 7 * 1 = 7
Therefore, the coordinates of A' are (14, 7).
Now let's find the coordinates of B':
x-coordinate of B' = 7 * x-coordinate of B = 7 * 4 = 28
y-coordinate of B' = 7 * y-coordinate of B = 7 * 3 = 21
Therefore, the coordinates of B' are (28, 21).
Finally, let's find the coordinates of C':
x-coordinate of C' = 7 * x-coordinate of C = 7 * (-2) = -14
y-coordinate of C' = 7 * y-coordinate of C = 7 * 5 = 35
Therefore, the coordinates of C' are (-14, 35).
In summary:
A' = (14, 7)
B' = (28, 21)
C' = (-14, 35)
To determine the scale factor for the dilation of triangle ABC, we can calculate the ratio of the distance between the original points and the distance between the corresponding points after dilation.
Let's start by finding the distance between points A and B:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-2 - 2)^2 + (2 - 1)^2)
= sqrt((-4)^2 + 1^2)
= sqrt(16 + 1)
= sqrt(17)
Now let's find the distance between points A' and B':
A'B' = sqrt((x2' - x1')^2 + (y2' - y1')^2)
= sqrt((-4 - 4)^2 + (4 - 2)^2)
= sqrt((-8)^2 + 2^2)
= sqrt(64 + 4)
= sqrt(68)
= 2 * sqrt(17)
The scale factor is the ratio of A'B' to AB:
scale factor = A'B' / AB
= (2 * sqrt(17)) / sqrt(17)
= 2
Therefore, the scale factor for the dilation of triangle ABC, with a center point of dilation at the origin, is 2.
To determine the scale factor used in the dilation of AB, we can calculate the ratio of the distance between the original points and the distance between the corresponding points after dilation.
The distance between points A and B can be found using the distance formula:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
AB = sqrt((2 - (-3))^2 + (-4 - 4)^2)
= sqrt(5^2 + (-8)^2)
= sqrt(25 + 64)
= sqrt(89)
The distance between the corresponding points A' and B' can also be found using the distance formula:
A'B' = sqrt((x2' - x1')^2 + (y2' - y1')^2)
A'B' = sqrt((4 - (-6))^2 + (-8 - 8)^2)
= sqrt(10^2 + (-16)^2)
= sqrt(100 + 256)
= sqrt(356)
The scale factor is the ratio of A'B' to AB:
scale factor = A'B' / AB
= sqrt(356) / sqrt(89)
To rationalize the denominator and simplify the expression, we can multiply the numerator and denominator by sqrt(89):
scale factor = (sqrt(356) / sqrt(89)) * (sqrt(89) / sqrt(89))
= sqrt(356 * 89) / 89
= sqrt(31684) / 89
= 178 / 89
Therefore, the scale factor used in the dilation of AB, with a center point of dilation at the origin, is 178/89.
thats incorrect
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 a dilation with a scale factor of 7 and a center point of dilation at the origin (0,0).
A' = (_)
B' = (_)
C' = (_)
Triangle ABC has vertices point A(2,1), point B(-2, 2), and point C(-3, -1). After dilation, triangle A'B'C' has vertices point A'(4, 2), point B'(-4, 4), and point C'(-6, -2). Determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0, 0).
The scale factor is __