Question

question 8 (multiple choice worth 1 points)
connor is constructing parallelogram abcd. he has plotted a at (-2, 4), b at (0, 3), and d at (-3, 2). which coordinate could be the location of point c?
c (0, 0)
c (0, 1)
c (-1, 1)
c (-1, 2)

Explanation:

Step1: Use the property of parallelogram

In a parallelogram \(ABCD\), \(\overrightarrow{AB}=\overrightarrow{DC}\).
The vector \(\overrightarrow{AB}=(0 - (- 2),3 - 4)=(2,-1)\).
Let the coordinates of point \(C\) be \((x,y)\). Then \(\overrightarrow{DC}=(x-(-3),y - 2)=(x + 3,y - 2)\).

Step2: Solve for \(x\) and \(y\)

Since \(\overrightarrow{AB}=\overrightarrow{DC}\), we have the following system of equations:
\(

$$\begin{cases}x+3 = 2\\y - 2=-1\end{cases}$$

\)
From \(x+3 = 2\), we get \(x=2-3=-1\).
From \(y - 2=-1\), we get \(y=-1 + 2=1\).

Answer:

\(C(-1,1)\)