Question

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Answer 1

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 $(x_{1},y_{1})$ and $(x_{1},y_{1})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
• The slope of a line which passes through point $(x_{1},y_{1})$ and $(x_{1},y_{1})$ is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
• The parallel lines have the same slopes
• The distance between the tow points $(x_{1},y_{1})$ and $(x_{1},y_{1})$ is $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

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

∴ $x_{1}$ = 0 and $x_{2}$ = 5

∴ $y_{1}$ = 0 and $y_{2}$ = -1

∴ $L=(\frac{0+5}{2},\frac{0+-1}{2})=(\frac{5}{2},\frac{-1}{2})$

∴ L = (2.5 , -0.5)

∵ M is the mid-point of BC

- Let B is the first point and C is the second point

∴ $x_{1}$ = 2 and $x_{2}$ = 5

∴ $y_{1}$ = 2 and $y_{2}$ = -1

∴ $M=(\frac{2+5}{2},\frac{2+-1}{2})=(\frac{7}{2},\frac{1}{2})$

∴ 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

∴ $x_{1}$ = 2.5 and $x_{2}$ = 3.5

∴ $y_{1}$ = -0.5 and $y_{2}$ = 0.5

∵ $m_{LM}=\frac{0.5-(-0.5)}{3.5-2.5}=\frac{1}{1}$

∴ The slope of LM is 1

- Let A is the first point and B is the second point

∴ $x_{1}$ = 0 and $x_{2}$ = 2

∴ $y_{1}$ = 0 and $y_{2}$ = 2

∵ $m_{AB}=\frac{2-0}{2-0}=\frac{2}{2}$

∴ 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

∴ $x_{1}$ = 2.5 and $x_{2}$ = 3.5

∴ $y_{1}$ = -0.5 and $y_{2}$ = 0.5

∵ $d_{LM}=\sqrt{(3.5-2.5)^{2}+(0.5--0.5)^{2}}=\sqrt{1+1}=\sqrt{2}$

∴ The length of LM is √2

- Let A is the first point and B is the second point

∴ $x_{1}$ = 0 and $x_{2}$ = 2

∴ $y_{1}$ = 0 and $y_{2}$ = 2

∵ $d_{AB}=\sqrt{(2-0)^{2}+(2-0)^{2}}=\sqrt{4+4}=2\sqrt{2}$

∴ The length of AB is 2√2

∵ $\frac{\sqrt{2}}{2\sqrt{2}}=\frac{1}{2}$

∴ 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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