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Geometry 101

December5

Here is a great tip to improve your Geometry skills – always add these extra labels to your axes – they will help you solve graphs far more easily!! Trust me, this is another H3 tip that DOES make a big difference in your Mathematics!!

Note 1: The y axes has the equation x=0. For example, if you have the graph of 2x+3y=12 then, when x=0 the equation is: 2(0)+3y=12 or y=4. So, this graph crosses the y-axis at 4! Easy As!!

Note 2: the y axis can be written as f(x). This means that the y value is a function of the x value. For example, in the graph (aka equation) of y=3x, when x is 4, y=3(4)=12. It is important that our growing mathematician understands that the y values are affected (changed) by whatever we plug into the x values. In other words, “y is a function of x” which we write mathematically as y=f(x). So, it is a good idea to label your axes as above to get into good Geometry habits!

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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