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secondary 2 | Maths
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Alex L
Alex L

secondary 2 chevron_right Maths chevron_right Singapore

Geometry: Reflections

I have the answer but please explain how to do it. Thanks

Date Posted: 3 years ago
Views: 449
J
J
3 years ago
y = 2x - 3

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
Eric Nicholas K
Eric Nicholas K
3 years ago
Or let’s put it another way.

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.
J
J
3 years ago
Not just y = x though

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