Calculate the co-ordinates of:-
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AP = AB/3
AP/AB = 1/3
So,
AP = x ; AB = 3x
Therefore: PB = AB - AP = 3x - x = 2x
Ratio = AP : PB = x : 2x = 1 : 2
Let coordinates of A be (x,0) and coordinates of B be (0,y)
Section formula
P(4,-2) = P [ (2x + 0) / 3 , (y + 0) / 3]
∴ 4 = 2x/3
x = 6
And,
-2 = y/3
y = -6
i) A(6,0)
ii) B(0, -6)
iii) AB = √[(6 - 0)² (0 + 6)²] = √[2(6^2)] = 6√2 units
iv) Ar.(triangle AOB) = 1/2 x AO x BO = 1/2 x 6 x 6 = 18 units²
(Pls find ao and bo yourself)
Hope I helped
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