Question #205460

Find the area of the triangle with the given vertices A(1, 3), B(-3, 5), and C with C = 2A. (3) (3.2) Use (3.1) to find the coordinates of the point D such that the quadrilateral ABCD is a paral- (3) lelogram.


1
Expert's answer
2021-06-12T00:48:12-0400

(3.1)


AB=31,53=4,2\overrightarrow{AB}=\langle-3-1, 5-3\rangle=\langle-4, 2\rangle

C=(2(1),2(3))C=(2(1), 2(3))

AC=2(1)1,2(3)3=1,3\overrightarrow{AC}=\langle2(1)-1, 2(3)-3\rangle=\langle1, 3\rangle

AB×AC=ijk420130=(4(3)2(1))k=14k\overrightarrow{AB}\times \overrightarrow{AC}=\begin{vmatrix} \vec i & \vec j & \vec k \\ -4 & 2 & 0 \\ 1 & 3 & 0 \end{vmatrix}=(-4(3)-2(1))\vec k=-14\vec k

=(4(3)2(1))k=14k=(-4(3)-2(1))\vec k=-14\vec k

AreaABC=12AB×AC=7(units2)Area_{ABC}=\dfrac{1}{2}|\overrightarrow{AB}\times \overrightarrow{AC}|=7(units^2)

Area of the triangle ABC is 7 square units.


(3.2)

Assume that the fourth vertex of parallelogram is D(x,y)D(x, y)

AB=DC=4,2\overrightarrow{AB}=\overrightarrow{DC}=\langle-4, 2\rangle

2x,6y=4,2\langle 2-x, 6-y\rangle=\langle-4, 2\rangle

x=6,y=4x=6, y=4


D(6,4)D(6, 4)



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS