If (1, p/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9), then show that the line 5x + 3y + 2 = 0 passes through the point (–1, 3p).
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Answer:
Since (1, p/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9)
Therefore, p/3 = (0 + 2/9)/2
p = 1/3
The line 5x + 3y + 2 = 0 passes through the point (–1, 1) as 5(–1) + 3(1) + 2 = 0
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Answer:
Joining BD, there are two triangles.
Area of quad ABCD = Ar △ABD + Ar △BCD
Ar △ABD = ½| (-5)(-5 - 5) + (-4)(5 - 7) + (4)(7 + 5) |
= 53 sq units
Ar △BCD = ½| (-4)(-6 - 5) + (-1)(5 + 5) + (4)(-5 + 6) |
= 19 sq units
Hence, area of quad ABCD = 53 + 19 = 72 sq units
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