Mathematics, 07.04.2021 09:20, mvazquez298

Given the points A (-3, -1), B (1, 4) C (4, -1) what is the x coordinate of D, if ABCD is a parallelogram?

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answered: xoxzyanya61

Given:

ABCD is a parallelogram, A(-3,-1), B(1,4), C(4,-1).

To find:

The x-coordinate of point D.

Solution:

Let the point D be (x,y).

We know that the diagonals of a parallelogram bisect each other. So, third midpoints are same.

Midpoint formula:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

In parallelogram ABCD, AC and BD are two diagonals.

Midpoint of AC = Midpoint of BD

$\left(\dfrac{-3+4}{2},\dfrac{-1+(-1)}{2}\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)$

$\left(\dfrac{1}{2},\dfrac{-2}{2}\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)$

$\left(\dfrac{1}{2},-1\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)$

On comparing both sides, we get

$\dfrac{1}{2}=\dfrac{1+x}{2}$

1=1+x

1-1=x

0=x

Similarly,

$-1=\dfrac{4+y}{2}$

-2=4+y

-2-4=y

-6=y

The coordinates of point D are (0,-6).

Therefore, the x-coordinate of point D is 0.

answered: Guest

answer is c

step-by-step explanation:

answered: Guest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

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Given the points A (-3, -1), B (1, 4) C (4, -1) what is the x coordinate of D, if ABCD is a parallel...