Question

question 4(multiple choice worth 1 points) (04.01 mc) 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: Recall parallelogram property

In parallelogram \(ABCD\), the mid - points of diagonals \(AC\) and \(BD\) coincide. The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).

Step2: Find mid - point of \(BD\)

Let \(B(0,3)\) and \(D(-3,2)\). Then the mid - point of \(BD\) is \(M_{BD}=(\frac{0+( - 3)}{2},\frac{3 + 2}{2})=(-\frac{3}{2},\frac{5}{2})\).

Step3: Let \(A(-2,4)\) and \(C(x,y)\)

The mid - point of \(AC\) is \(M_{AC}=(\frac{-2 + x}{2},\frac{4 + y}{2})\).

Step4: Equate mid - points

Since \(M_{BD}=M_{AC}\), we have the following system of equations:
\(\frac{-2 + x}{2}=-\frac{3}{2}\) and \(\frac{4 + y}{2}=\frac{5}{2}\).
For \(\frac{-2 + x}{2}=-\frac{3}{2}\), cross - multiply: \(-2 + x=-3\), then \(x=-3 + 2=-1\).
For \(\frac{4 + y}{2}=\frac{5}{2}\), cross - multiply: \(4 + y = 5\), then \(y=5 - 4 = 1\). So \(C(-1,1)\).

Answer:

C. C (-1, 1)