Graphs can be used to support geometric information: vertices (or corners) can be defined by coordinates, edges can be defined by equations or line segments, and the centre of a circle can be defined by a coordinate.
A rectangle has vertices at coordinates (-8,1), (4,1) and (4,-2).
What is the coordinate of the fourth vertex?
There must be two matching `x`-coordinates and two matching `y`-coordinates. The missing values are -8 for `x` and -2 for `y`. The missing coordinate is (-8,-2).
Answer: (-8, -2)
A triangle is defined by three lines:
`y=3x+4` , `y = -2x -6` and `x=2`
What is the length between the highest and lowest points of the triangle?
Note that the line `x=2` is vertical
For `y=3x+4` when `x=2` then `y`=10
The top coordinate is `(2, 10)`
For `y = -2x-6` when `x=2` then `y`=-10
The bottom coordinate is (2, -10)
Vertical distance is 10 - -10 = 20
If unsure, sketch the graph first
Answer: 20