Respuesta :
Answer: The required values are x = 2 and y = 2.
Step-by-step explanation: Given that the points A, B and C are collinear on AC and AB : BC = 3 : 4.
Also, A is located at (x, y), B is located at (4, 1) and C is located at (12,5).
We are to find the values of x and y.
We know that
the co-ordinates of a point that divides a line segment with endpoints (a, b) and (c, d) in the ratio m : n are given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
According to the given information, we get
[tex]4=\dfrac{3\times 12+4\times x}{3+4}\\\\\\\Rightarrow 4=\dfrac{36+4x}{7}\\\\\Rightarrow 36+4x=28\\\\\Rightarrow 4x=8\\\\\Rightarrow x=\dfrac{8}{4}\\\\\Rightarrow x=2[/tex]
and
[tex]1=\dfrac{3\times5+4\times y}{3+4}\\\\\\\Rightarrow 1=\dfrac{15+4y}{7}\\\\\Rightarrow 15+4y=7\\\\\Rightarrow 4y=8\\\\\Rightarrow y=\dfrac{8}{4}\\\\\Rightarrow y=2.[/tex]
Thus, the required values are x = 2 and y = 2.
Using line segments, it is found that:
- The value of x is -2.
- The value of y is -2.
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- Point A is located at (x,y).
- Point B is located at (4,1).
- Point C is located at (12,5).
- AB:BC=3/4 means that:
[tex]B - A = \frac{3}{4}(C - B)[/tex]
- This is used to find the x and y-coordinates of A.
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- The x-coordinate of A is x.
- The x-coordinate of B is 4.
- The x-coordinate of C is 12.
Thus:
[tex]B - A = \frac{3}{4}(C - B)[/tex]
[tex]4 - x = \frac{3}{4}(12 - 4)[/tex]
[tex]4 - x = 6[/tex]
[tex]x = -2[/tex]
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- The y-coordinate of A is y.
- The y-coordinate of B is 1.
- The y-coordinate of C is 5.
Thus:
[tex]B - A = \frac{3}{4}(C - B)[/tex]
[tex]1 - y = \frac{3}{4}(5 - 1)[/tex]
[tex]1 - y = 3[/tex]
[tex]y = -2[/tex]
A similar problem is given at https://brainly.com/question/24647154
