Straight Line Spin
Can you draw the graph of $y=x$ after it has been rotated $90$ degrees clockwise about $(1,1)$?
Age
11 to 14
Challenge level
Problem
Draw a diagram which shows the graph of $y=x$ after it has been rotated $90^{\circ}$ clockwise about the point $(1,1)$.
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer:
Image
Geometrically:
Image
Image
Image
The lines are perpendicular, so the new line slopes downwards at $45^\circ$, so its gradient is $-1$
It passes through $(1,1)$ so it also passes through $(0,2)$
Equation $y=-x+2$