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:. www-awu.aleks.com/alekscgi/x/Isl.exe/10_u-IgNsIkr7j8P3jH-IBluonLF7GsfmBxLWEUDiYeCmloA5WJ3
Unit 7 Homework
Question 10 of 20 (1 point) | Question Attempt: 1 of Unlimited
6
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✓9
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13
Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.
Check

$\therefore$ www-awu.aleks.com/alekscgi/x/Isl.exe/ $10$ _u-IgNsIkr $7$ j $8$ P $3$ jH-IBluonLF $7$ GsfmBxLWEUDiYeCmloA $5$ WJ $3$ $\newline$ Unit $7$ Homework $\newline$ Question $10$ of $20$ ( $1$ point) | Question Attempt: $1$ of Unlimited $\newline$ $6$ $\newline$ $7$ $\newline$ $8$ $\newline$ $\checkmark 9$ $\newline$ $10$ $\newline$ $11$ $\newline$ $12$ $\newline$ $13$ $\newline$ Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex. $\newline$ Check

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Complex conjugate theorem

Full solution

Q.

\therefore

www-awu.aleks.com/alekscgi/x/Isl.exe/

10

_u-IgNsIkr

7

j

8

P

3

jH-IBluonLF

7

GsfmBxLWEUDiYeCmloA

5

WJ

3

\newline

Unit

7

Homework

\newline

Question

10

of

20

(

1

point) | Question Attempt:

1

of Unlimited

\newline

6

\newline

7

\newline

8

\newline

\checkmark 9

\newline

10

\newline

11

\newline

12

\newline

13

\newline

Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.

\newline

Check

Identify Parallelogram Properties: The parallelogram has opposite sides that are equal and parallel. We can use the given three vertices to find the fourth by using vector addition.
Find Fourth Vertex using Vector Addition: Let's say the given vertices are $A$ , $B$ , and $C$ , and we need to find $D$ . If we assume $A$ and $C$ are opposite vertices, then we can find $D$ by using the fact that the diagonals of a parallelogram bisect each other.
Calculate Midpoint of Diagonal AC: We can calculate the midpoint $M$ of the diagonal $AC$ , which will also be the midpoint of $BD$ . Then we can use the midpoint formula $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ where $(x_1, y_1)$ are the coordinates of $A$ and $(x_2, y_2)$ are the coordinates of $C$ .
Use Midpoint Formula for Coordinates of D: Let's say the coordinates of A are $(x_1, y_1)$ , B are $(x_2, y_2)$ , and C are $(x_3, y_3)$ . We calculate the midpoint M of AC using $M = \left(\frac{x_1 + x_3}{2}, \frac{y_1 + y_3}{2}\right)$ .
Find Coordinates of D using Midpoint Formula: Now, we can find the coordinates of D by using the fact that M is also the midpoint of BD. So, $D = (2M_x - x_2, 2M_y - y_2)$ where $M_x$ and $M_y$ are the $x$ and $y$ coordinates of M, respectively.
Find Coordinates of D using Midpoint Formula: Now, we can find the coordinates of D by using the fact that M is also the midpoint of BD. So, $D = (2M_x - x_2, 2M_y - y_2)$ where $M_x$ and $M_y$ are the $x$ and $y$ coordinates of M, respectively.We plug in the values of M and B into the formula for D and solve for the coordinates of D.

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