Area ABC = 59.9998

The best way to tackle this problem is to draw the question on a graph and plot each point.

Once you’ve done this you’ll notice that AO is the radius (or half a diameter). Using coordinates, AO is (-1,-8). In triangle form this means that one length of the triangle AO is 8 and the other is 1. By using a^2=b^2+c^2, AO is the square root value of 8^2 + 1^2 which is 8.06226. This means AC is 2 x AO = 16.1245.

Looking at your graph, we can see the triangle ABC. Use the above method to work out the length of AB and BC:

AB: (-8,-4) => square root of 8^2+4^2= 8.94427
AC: (6,-12) => square root of 6^2+12^2= 13.4164

Now we have the lengths of all three sides of the triangle ABC. *Remember that drawing your working out will always help*. There are multiple methods but the easiest in my opinion is using trigonometry by calculating at least one angle of the triangle. Using sinx=opposite/hypotenuse, sinACB=BC/AC, sinACB=8.94427/16.1245, ACB=33.6901. 

Using Area ABC=0.5 x BC x AC x sinC, Area ABC=0.5 x 13.4164 x 16.1245 x sin(33.6901) = 59.9998

Maths

The line segment AB is a chord of a circle centre (2,-1) where A and B are (3,7) and (-5,3) respectively. AC is a diameter of the circle. Find the area of ABC

If the line is parallel then the gradient will be the same on all equations therefore y=mx+c and m=2 for the gradient.

If x=0 and y=7 at the point the line goes through, substituting these values in gives 7=0+c, rearrange to get c=7.

Therefore the line is y=2x+7

How do you work out what the equation of the parallel line to my=2x+3 and passes through (0,7) is

You have one of two approaches here:

1. Calculate the value of 4% which equates to 0.04 x £14120 = £564.80. Simply add the value to the full amount: £14120 + £564.80 = £14684.80.

2. A 4% increase in a value can be calculated by multiplying your initial value by 1.04 (not to be confused with a 4% decrease which is calculated by multiplying your initial value by 96%). So, 1.04 x £14120 = £14684.80.

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