Determine the scale factor used in the dilation of line segment AB, centered at the origin
it's 3 guys
To determine the scale factor used in the dilation of line segment AB, centered at the origin, you need to know the lengths of both the original line segment AB and the dilated line segment.
The scale factor, denoted as "k," is found by dividing the length of the dilated line segment by the length of the original line segment. Mathematically, it can be expressed as:
k = Length of Dilated Line Segment / Length of Original Line Segment
To find the lengths of the line segments, you can use the distance formula. The formula to find the distance between two points (x1, y1) and (x2, y2) is:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
You can substitute the coordinates of points A and B into the distance formula to find the lengths of the line segments AB and the dilated line segment.
Once you have found the lengths, you can calculate the scale factor by dividing the length of the dilated line segment by the length of the original line segment.
To determine the scale factor used in the dilation of line segment AB, centered at the origin, we need to know the coordinates of the original line segment AB and the coordinates of the dilated line segment A'B'.
The scale factor (k) is the ratio of the length of the dilated line segment to the length of the original line segment. Mathematically, it can be calculated as follows:
k = |A'B'| / |AB|
To find the length of a line segment, we can use the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
So, to find the length of line segment AB, we substitute the coordinates of point A (x1, y1) and point B (x2, y2) into the distance formula:
|AB| = √((x2 - x1)^2 + (y2 - y1)^2)
Similarly, we can find the length of line segment A'B' using the coordinates of point A' (x1', y1') and point B' (x2', y2'):
|A'B'| = √((x2' - x1')^2 + (y2' - y1')^2)
Finally, we can calculate the scale factor (k) by dividing the length of the dilated line segment by the length of the original line segment:
k = |A'B'| / |AB|
Once you have the coordinates of both the original and dilated line segments, substitute them into the formulas above and perform the calculations to obtain the scale factor.
, from a length of 8 to a length of 12
The scale factor used in the dilation of line segment AB is 1.5.