Exercises Coordinate Geometry

Solutions

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2. y = 4x − 8 meets the x-axis means that y = 0
by solving 4x − 8 = 0, it appears that x = 2
⇒ the line meets the x-axis at the point A(2, 0)

We'll now find the equation of the line with gradient 3, passing through the point A
The gradient m = ^{change in y}/_{change in x} = ³/₁, which means the line passes through another point B(1, 3) with A(2, 0) as origin. (see Plot 1)



Plot 1




3. y = − 2x + 8 meets the y-axis means that x = 0
⇒ y = − 2(0) + 8 and y = 8
The point met is B(0, 8)
The other line passing, with gradient 2 has B as origin. (see Plot 2)



Plot 2


4. y = ¹/₂·x + 6 meets the x-axis means that y = 0
then, y = ¹/₂·x + 6 = 0 ⇒ x = − 12
if another line passes through C, its equation should be written y = ²/₃·x + 6 (see Plot 3)
The second equation colud the be written: ²/₃·x − y + 6 = 0, with a = ²/₃, b = −, c = 6.



Plot 3



5. Just do it like the previous exercises !!!




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6. Just do it like the previous exercises !!!

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