In the figure, lines l, m, and n are parallel. A classmate says you can use the corollary to the side-splitter theorem to find x
. explain your classmate's error
1 answer:
The issue with using the side-splitter to solve for x is that the side-splitter theorem is used to find lengths of the sides being split by parallel lines. In this case, the x is on a line that is parallel and thus could not be solved for using this theorem.
If we created a triangle where the tops of the non-parallel lines connected, we would be able to compare the following and solve:
However, none of this would help us solve for x using this theorem.
If we created a triangle where the tops of the non-parallel lines connected, we would be able to compare the following and solve:
However, none of this would help us solve for x using this theorem.
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3:5 ratio mean there are 8 "parts" (3 + 5 = 8)
The distance between the x-coordinates is |-3 - 5| = 8.
So each "part" is 8/8 = 1 unit long in the x-direction.
You want I to be 3(1) = 3 units from D, so the x-coordinate of I is -3 + 3 = 0.
Same deal for y.
|2 - 5| = 3 is the distance between D and E
Each part is 3/8.
3(3/8) = 9/8
2 + 9/8 = 25/8
So the point I is (0, 25/8)
The distance between the x-coordinates is |-3 - 5| = 8.
So each "part" is 8/8 = 1 unit long in the x-direction.
You want I to be 3(1) = 3 units from D, so the x-coordinate of I is -3 + 3 = 0.
Same deal for y.
|2 - 5| = 3 is the distance between D and E
Each part is 3/8.
3(3/8) = 9/8
2 + 9/8 = 25/8
So the point I is (0, 25/8)