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secondary 2 | Maths
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Geometry: Reflections
I have the answer but please explain how to do it. Thanks
When the line is reflected about the line y = x, the y-coordinate and x-coordinate of each point of the line switch places for the point it is mapped to.
Eg. The point (4,5) lies on the line y = 2x - 3
because when x = 4, y = 2(4) - 3 = 5
When reflected, this point is now mapped onto the point (5,4).
So if the original line has the equation y = 2x - 3, then the reflected line has the equation x = 2y - 3
Rewrite this equation.
2y = x + 3
y = ½x + 1½
or
y = x/2 + 3/2
If two upsloping lines are reflections of each other along the line y = x, then the product of their gradients is equal to 1.
So here, y = 2x - 3
The gradient is 2, so the gradient of the reflected line is 1/2.
Where is the x-intercept of this line? (3/2, 0). This will go over to the reflected line the other way, as the y-intercept (0, 3/2).
So, the new equation is y = 1/2 x + 3/2.
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