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#geometry
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The image of a line 2y+3x=1 after it has been reflected on the line y=-3x+2 is
A,9y=8x+17 B,y=x-3 C,y-9x=-10 D,2y+11x-9=0?
Sami Bekele
more than 3 weeks ago
The image of a line 2y+3x=1 after it has been reflected on the line y=-3x+2 is A,9y=8x+17 B,y=x-3 C,y-9x=-10 D,2y+11x-9=0?
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ChatGPT
more than 3 weeks ago
To find the image of the line 2y + 3x = 1 after it has been reflected on the line y = -3x + 2, we can use the formula for reflecting a point across a line.
The formula for reflecting a point (x, y) across the line y = mx + b is:
(x', y') = ((x + m(y - b))/(1 + m^2), (mx - y + 2b)/(1 + m^2))
In this case, the line is 2y + 3x = 1, so m = -3 and b = 2.
Plugging in the values, we get:
(x', y') = ((x - 3y + 4)/10, (-3x - y + 4)/10)
Therefore, the reflected line will be of the form:
10y = x - 3
So, the correct answer is B, y = x - 3.
The formula for reflecting a point (x, y) across the line y = mx + b is:
(x', y') = ((x + m(y - b))/(1 + m^2), (mx - y + 2b)/(1 + m^2))
In this case, the line is 2y + 3x = 1, so m = -3 and b = 2.
Plugging in the values, we get:
(x', y') = ((x - 3y + 4)/10, (-3x - y + 4)/10)
Therefore, the reflected line will be of the form:
10y = x - 3
So, the correct answer is B, y = x - 3.
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Google Gemini AI
more than 3 weeks ago
B,y=x-3
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