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secondary 3 | E Maths
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Date Posted: 5 years ago
Views: 303
eqn of line:
(y+6)/(x-1) = (-6-6)/(1-7) = 2
y + 6 = 2x - 2
y = 2x - 8
x-intercept is when y = 0,
2x - 8 = 0
x = 4
(a) k = 4
(b)
AP = √[(1-4)² + (-6-0)²]
= √(9 + 36) =√45
PB = √[(4-7)² + (0-6)²]
= √(9 + 36) =√45
AP = PB (shown)
(y+6)/(x-1) = (-6-6)/(1-7) = 2
y + 6 = 2x - 2
y = 2x - 8
x-intercept is when y = 0,
2x - 8 = 0
x = 4
(a) k = 4
(b)
AP = √[(1-4)² + (-6-0)²]
= √(9 + 36) =√45
PB = √[(4-7)² + (0-6)²]
= √(9 + 36) =√45
AP = PB (shown)
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For (a):
1. Calculate the gradient of the line using the 2 given points, followed by substituting 1 point into the general line equation (y=mx + c) to find the y-intercept and subsequently the equation of the line.
2. Substitute the y-coordinate of P (which is 0) into the equation of the line to find the x-coordinate (which is k)
For (b):
1. Find the length of AP using pythagoras theorem (observe the respective coordinates)
2. Find length of PB using pythagoras theorem (observe their coordinates as well)
3. Show that they are equal.
1. Calculate the gradient of the line using the 2 given points, followed by substituting 1 point into the general line equation (y=mx + c) to find the y-intercept and subsequently the equation of the line.
2. Substitute the y-coordinate of P (which is 0) into the equation of the line to find the x-coordinate (which is k)
For (b):
1. Find the length of AP using pythagoras theorem (observe the respective coordinates)
2. Find length of PB using pythagoras theorem (observe their coordinates as well)
3. Show that they are equal.
Date Posted:
5 years ago
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