Date | May Example question | Marks available | 9 | Reference code | EXM.1.SL.TZ0.4 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 0 |
Command term | Find | Question number | 4 | Adapted from | N/A |
Question
The diagram below is part of a Voronoi diagram.
Diagram not to scale
A and B are sites with B having the co-ordinates of (4, 6). L is an edge; the equation of this perpendicular bisector of the line segment from A to B is y=−2x+9y=−2x+9
Find the co-ordinates of the point A.
Markscheme
Line from A to B will have the form y=12x+cy=12x+c M1A1
Through (4,6)⇒c=4(4,6)⇒c=4 so line is y=12x+4y=12x+4 M1A1
Intersection of y=−2x+9y=−2x+9 and y=12x+4y=12x+4 is (2, 5) M1A1
Let A=(p,q)A=(p,q) then (2,5)=(p+42,q+62)⇒p=0,q=4(2,5)=(p+42,q+62)⇒p=0,q=4 M1A1A1
A=(0,4)A=(0,4)
[9 marks]