Coordinate Geometry

P124 q 23

For parts (i) through (iv) first write down the relevant formula, then plug in your values.
Watch out for the negative coordinates - say for example, when you are finding slope x2-x1 is going to be 6 - (-2) = 6+2 = 8

For part (v) remember what "equation of a line" means. It is a rule for being on a line.
For example - is the point (2,1) on the line 2x + 3y = 7?
Sub in for x and y: 2(2) + 3(1) = 7 which is true, so the point (2,1) is on the line.
Is the point (5,-1) on the line. Sub in and make sure you can figure out that yes, it is.

For part (vi) remember the rule for perpendicular slopes. If two lines are perpendicular, their slopes multiply to give -1 (or put another way, the product of their slopes is -1).
So if you have the slope of one line, you find the slope of the perpendicular line by inverting and changing the sign. If the slope of the first line is -2, then the slope of the perpendicular line is ½.

Part (viii) can be done using simultaneous equations.

For part (ix) draw a rough diagram if you haven't already done so. Axial symmetry in the line ab means that the line ab acts as a mirror. Where will the image of d be? A clue is to use translations.

For part (x) you are finding the points where the line crosses the X and Y axes. Remember that every point on the X axis has the coordinate (something,0).
You can work out the "something" by subbing y=0 in the equation of the line ab (see ans to part iv).

Finally, make sure that you use this question as an opportunity to revise all the formulae you need to know.

Really finally, don't forget your geometry sets tomorrow!