RI sec 3 1997 EOY P1 Q9
A line passing through the points (-5, w) and (3, 4) is parallel to 5y - 4x - 14 = 0. Find the value of w.
This line cuts the x-axis at A and y-axis at B. Find the area of ΔOAB where O is the origin.
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Answer:
5y - 4x - 14 = 0
5y = 4x + 14
y = 4x/5 + 14/5
Thus, equation of line is y = 4x/5 + c
Sub x=3, y=4
4 = 4(3)/5 + c
c = 8/5
Thus, equation of line is y = 4x/5 + 8/5
Sub x=-5, y=w
w = 4(-5)/5 + 8/5
w = -12/5
When y = 0, 4x/5 + 8/5 = 0
4x/5 = -8/5
x = -2
==> A: (-2,0)
When x = 0, y = 8/5
==> B: (0, 8/5)
Thus, using shoelace formula,
area =
= 1.6 units²
