A man is listening to his radio at the top of a mountain where the altitude is 4500 feet
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The coordinates of L are (2.5 , -0.5) and the coordinates of M are (3.5 , 0.5)
Line LM is parallel to line AB because they have same slopes
The line LM is half of line AB because √2 is half of 2√2
Step-by-step explanation:
Let us revise some rules:
- The coordinates of the mid-point of a segment whose endpoints are
and
- The slope of a line which passes through point
- The parallel lines have the same slopes
- The distance between the tow points
In Δ ABC
∵ A = (0 , 0) , B = (2 , 2) , C = (5 , -1)
∵ L is the mid-point of AC
- Let A is the first point and C is the second point
∴ = 0 and
= 5
∴ = 0 and
= -1
∴
∴ L = (2.5 , -0.5)
∵ M is the mid-point of BC
- Let B is the first point and C is the second point
∴ = 2 and
= 5
∴ = 2 and
= -1
∴
∴ M = (3.5 , 0.5)
The coordinates of L are (2.5 , -0.5) and the coordinates of M are (3.5 , 0.5)
Let us find the slopes of LM and AB
- Let L is the first point and M is the second point
∴ = 2.5 and
= 3.5
∴ = -0.5 and
= 0.5
∵
∴ The slope of LM is 1
- Let A is the first point and B is the second point
∴ = 0 and
= 2
∴ = 0 and
= 2
∵
∴ The slope of AB is 1
∵ The slope of LM is equal to the slope of AB
- Parallel lines have equal slopes
∴ LM // AB
Line LM is parallel to line AB because they have same slopes
Let us find the lengths of LM and AB
- Let L is the first point and M is the second point
∴ = 2.5 and
= 3.5
∴ = -0.5 and
= 0.5
∵
∴ The length of LM is √2
- Let A is the first point and B is the second point
∴ = 0 and
= 2
∴ = 0 and
= 2
∵
∴ The length of AB is 2√2
∵
∴ LM is half AB
The line LM is half of line AB because √2 is half of 2√2
Learn more:
You can learn more about the triangles in brainly.com/question/1479138
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