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mixas84 [53]
4 years ago
6

Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?

Mathematics
2 answers:
grandymaker [24]4 years ago
6 0
Only B.
...............
Viefleur [7K]4 years ago
3 0
I think the answer is B
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Gandalf the Grey started in the Forest of Mirkwood at a point P with coordinates (3, 0) and arrived in the Iron Hills at the poi
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Answer:

Turning point has coordinates \left(\dfrac{27}{13},\dfrac{8}{13}\right)

Step-by-step explanation:

Gandalf the Grey started in the Forest of Mirkwood at a point P(3, 0) and began walking in the direction of the vector \vec{v}=-3i+2j. The coordinates of the vector v are (-3,2). Then he changed the direction at a right angle, so he was walking in the direction of the vector \vec{u}=2i+3j (vectors u and v are perpendicular).

Let B(x,y) be the turning point. Find vectors PB and BQ:

\overrightarrow{PB}=(x-3,y-0)\\ \\\overrightarrow {BQ}=(5-x,5-y)

Note that vectors v and PB and vectors u and BQ are collinear, so

\dfrac{x-3}{-3}=\dfrac{y}{2}\\ \\\dfrac{5-x}{2}=\dfrac{5-y}{3}

Hence

2(x-3)=-3y\Rightarrow 2x-6=-3y\\ \\3(5-x)=2(5-y)\Rightarrow 15-3x=10-2y

Now solve the system of two equations:

\left\{\begin{array}{l}2x+3y=6\\ -3x+2y=-5\end{array}\right.

Multiply the first equation by 3, the second equation by 2 and add them:

3(2x+3y)+2(-3x+2y)=3\cdot 6+2\cdot (-5)\\ \\6x+9y-6x+4y=18-10\\ \\13y=8\\ \\y=\dfrac{8}{13}

Substitute it into the first equation:

2x+3\cdot \dfrac{8}{13}=6\\ \\2x=6-\dfrac{24}{13}=\dfrac{54}{13}\\ \\x=\dfrac{27}{13}

Turning point has coordinates \left(\dfrac{27}{13},\dfrac{8}{13}\right)

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