The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ? Use the distance formula to help you decide: .
To find the slope (m) of the line AB, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Given that point A is (2, 2) and point B is (3, 8), we can substitute these values into the formula:
m = (8 - 2) / (3 - 2)
m = 6 / 1
m = 6
So the slope of line AB is 6.
To find the length of AB, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Again, substituting the coordinates of A and B:
d = √((3 - 2)^2 + (8 - 2)^2)
d = √(1^2 + 6^2)
d = √(1 + 36)
d = √37
Therefore, the length of line AB is √37.
To find the slope of AB, we can use the slope formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) are the coordinates of point A and (x2, y2) are the coordinates of point B.
In this case, A(2, 2) has coordinates (x1, y1) = (2, 2) and B(3, 8) has coordinates (x2, y2) = (3, 8).
Plugging these values into the slope formula:
m = (8 - 2) / (3 - 2) = 6 / 1 = 6.
Therefore, the slope of AB is 6.
To find the length of AB, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2),
where (x1, y1) are the coordinates of point A and (x2, y2) are the coordinates of point B.
In this case, A(2, 2) has coordinates (x1, y1) = (2, 2) and B(3, 8) has coordinates (x2, y2) = (3, 8).
Plugging these values into the distance formula:
d = √((3 - 2)^2 + (8 - 2)^2) = √(1 + 36) = √37.
Therefore, the length of AB is √37 units.
The slope does not change.
Multiply all coordinates by 3.5:
A(7, 7), B(10.5, 28).
m = (28-7)/(10.5-7) =
L = Sqrt((10.5-7)^2 + (28-7)^2) =