Geometry

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You are given the cordinates of the four points
A (6,2), B(2.4), C (-6, -2) and D (-2,-4).

Show that the equation of the line DA is 4y-3x = -10

• Geometry -

sub in the points A(6,2) and D(-2,-4)
into 4y - 3x = -10

for (6,2)
LS = 4(2) - 3(6) = -10 = RS
for (-2,-4)
LS = 4(-4) - 3(-2) = -10 = RS

YES , the equation of DA is 4y-3x = -10

Where do the other two points enter the picture ?

• Geometry -

Could you please explain that in full, as im really struggling to understand. The other two points were for calculating gradients AB, CB, DC and DA but i got that.

Thanks reiny!

• Geometry -

Is there a way of simplifying the equation 4y-3x=-10 to y=0.75x - 2.5, then proving that is the equation for DA?

• Geometry -

I don't know how much further I can explain it.
Since both points satisfy the given equation, the equation must be the correct one
All I did was replace the x and y in the equation with the x and y of each of the points
LS stands for left side of the equation
RS stands for the right side.

in
4y - 3x = -10
4y = 3x - 10
y = (3/4)x - 10/4
or
y = .75x - 2.5

The last equation and the starting equation are really the same thing.
Subbing in either one gives you the same result

e.g.
sub in (6,2) into y = .75x - 2.5
LS = 2
RS = .75(6) - 2.5 = 4.5 - 2.5 = 2
since LS = RS , the point lies on the equation.

I will let you sub in the second point in the same way.
Let me know if you did NOT get it.

• Geometry -

What is RS and LS?

• Geometry -

Did you not read my reply ? I explained what they are.

• Geometry -

Im sorry!!! Its so late and im half asleep. Worse time to do maths. I get it reiny!!!!!!!
Thank you
So the second point is -4 = -4
therefore it must be the correct equation as both points satisfy the equation?

• Geometry -

You got it.

• Geometry -

Many thanks

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