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4 years ago

Does the given equation of line form parallel lines or not

Mathematics

1 answer:

malfutka [58]4 years ago

5 0

$k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2$

$k:x+4y=10\ \ \ |-x\\\\4y=-x+10\ \ \ \ |:4\\\\y=-\dfrac{1}{4}x+\dfrac{10}{4}\to m_1=-\dfrac{1}{4}\\\\l:3x-2y=5\ \ \ \ |-3x\\\\-2y=-3x+5\ \ \ \ |:(-2)\\\\y=\dfrac{3}{2}x-\dfrac{5}{2}\to m_2=\dfrac{3}{2}$

$m_1\neq m_2\to\text{ no parallel}\\\\m_1\cdot m_2=-\dfrac{1}{4}\cdot\dfrac{3}{2}\neq-1\to\text{ no perpendicular}$

Answer: NOT PARALLEL

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Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the

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Answer: The answers are

(i) The slope of segments DE and AC is not 0.

(ii) The coordinates of D and E were found using the Midpoint Formula.

Step-by-step explanation: We can easily see in the proof that the co-ordinates of D and E were found using the mid-point formula, not distance between two points formula. So, this is the first flaw in the Gina's proof.

Also, we see that the slope of line DE and AC, both are same, not equal to 0 but is equal to

$\dfrac{y_2}{x_2},$

which is 0 only if $y_2=0.$

So, this is the second mistake.

Thus, the statements that corrects the flaw in Gina's proof are

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(ii) The coordinates of D and E were found using the Midpoint Formula.

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In this problem, they want you to take the triangle and flip it over the line. It's going to create a mirror image on the other side.

That line is y = x, which is just a basic plain diagonal line that goes bottom left to top right.

To start, I would ALWAYS write down the coordinates of the original triangle.

D (-1, 3)

F (-3, 1)

E (-1, 1)

Now, <em>here's the trick</em>

Anytime it asks you to flip over Y = X, <em>remember</em> that you just flip X and Y!!!

(X, Y) --> (Y, X)

Your new coordinate points are going to be:

D (3, -1)

F (1, -3)

E (1, -1)

Now, just plot those points, connect the dots, and you have your new, mirrored triangle!

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