If coordinates of A,B and C are respectively (4,0),(6,0) and(12,1) and area of triangle BCD/area of triangle ABC=5/2 ,then AD/AB=? and find the coordinates of D?
Answers
Answer:
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Answer:
(Funny thing is that I just had this exact math for homework.)
AD/AB=3/2
The coordinates of D is (1,0)
Step-by-step explanation:
First, draw a perpendicular CE on the x-axis from C which will act as the height of of both triangles.
Now, ΔBCD/ΔABC=(1/2×CE×BD)/(1/2×CE×AB)
=BD/AB
∵ΔBCD/ΔABC=5/2
∴BD/AB=5/2
⇒(BD-AB)/AB=(5-2)/2
∴AD/AB=3/2 [∵AD=BD-AB]
Let the coordinate of D be (x,y)
since, D is situated on x-axis
ordinate of D is 0
∵AD/AB=3/2
then, A intersects BD in 3:2 ratio.
∴abcissa of A = 18+2x/5
∴18+2x/5=4
⇒2x=2
∴x=1
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