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Georgia [21]
3 years ago
15

A,B and C are the vertices of a triangle A has coordinates (4,6) B has coordinates (2,-2) C has coordinates (-2,-4) D is the mid

point of AB E is the midpoint of AC Prove that DE is parallel to BC
Mathematics
1 answer:
polet [3.4K]3 years ago
8 0

Answer:

Segments DE and BC have equal slopes, showing that segments DE and BC are parallel

Step-by-step explanation:

Here we have the coordinates as follows

The coordinates of A is (4, 6)

The coordinates of B is (2, -2)

The coordinates of C is (-2, -4)

Therefore, the coordinates of D the midpoint AB is ((4 + 2)/2, (6 - 2)/2) which gives;

The coordinates of D is (3, 2)

Similarly, the coordinates of E the midpoint AC is ((4 - 2)/2, (6 - 4)/2) which gives;

The coordinates of E is (1, 1)

To prove that segment DE is parallel to segment BC, e show that the slopes of the two segments are equal as follows;

Slope \, of \, a \, segment = \frac{Change \, in \, the\ y \, coordinates}{Change \, in \, the\, x \, coordinates}

Slope \, of \, segment \  DE =\frac{2 - 1}{3-1} = \frac{1}{2}

Slope \, of \, segment \  BC =\frac{-2 - (-4)}{2-(-2)} = \frac{2}{4} =\frac{1}{2}

Therefore, the slopes of segments DE and BC are equal, which shows that segment DE is parallel to BC.

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Answer:

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Marina86 [1]

Answer:

y = 2/3x - 3

Step-by-step explanation:

First let's look at what slope-intercept form is.

y = mx + b

m is the slope, which in this case is 2/3

b is the y-intercept, which we will find later.

Now that we have identified the parts of the equation, let's plug in what we know. Use the point given for your x and y values.

y = mx + b

1 = 2/3(6) + b

Let's simplify this to find b.

[multiply] 1 = 4 + b

[subtract 4]

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We now have our b-value, which is also our y-intercept. Plug in this value into the standard slope-intercept equation.

y = 2/3x - 3

This is your equation.

Check this by plugging in the point again.

1 = 2/3(6) - 3

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[subtract]

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This expression is true; therefore, your answer is correct.

Hope this helps!

7 0
3 years ago
The area of a rectangle or a 48 square inches the length is 8 inches what is the measure of its width
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this the anwers

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