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Geometric Information on a Graph

Geometric Information on a Graph

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.

Example 1

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).

Rectangle on a graph

Answer: (-8, -2)

Example 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

Triangle on a graph to get the longest side

Answer: 20