Question

Is my work correct?

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Answer 1

See below.

Explanation:

You have calculated the correct coordinates, but you have made an error with the graph. You have not plotted the point `(12,7)` in the correct place. I have marked the correct position with the black line.

The correct geometric figure is a rectangle, not a rhombus.

This can be shown by the following.

Take a pair of intersecting lines, say the first pair:

`y=2x+13 and x+2y=-14`

Rearrange so both are in the form: `y=mx+b`

`y=2x+13`

`y=-1/2x-7`

If we find the product of the two gradients:

`2xx-1/2=-1`

Whenever two line are perpendicular, the product of their gradients is `-1`.

If you check the other pairs on intersecting lines, you will find they are also perpendicular. This means the geometric figure has four right angles, and its sides are not all the same length,so it can't be a rhombus.

The length of the sides can be found and checked using the distance formula.

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

Some of this may be above the level you are currently at. Maybe you have just been asked to find the figure by looking at the graph, in which case you can see it is a rectangle. You probably were thrown by the fact that one of the coordinates wasn't plotted correctly and the figure is at an angle, this can often trip you up.