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Question
Δ AMT ∼ ΔAHE. In Δ AMT, MA = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(MA)/(HA) = 7/5`. construct Δ AHE.
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Solution
Drawing Δ AMT of given measure
Drawing a ray making an acute angle at A with side AM. mark points `A_1 , A_2 , ...., A_7 " such that " A A_1 = A_1A_2 = A_2 A_3 = A_3 A_4 = A_4 A_5 = A_5 A_6 = A_6 A_7` Joining A7 and M and drawing seg A5 H parallel to A7M, where H is the point on AM
Drawing HE || side MT
Δ AHE is the required triangle similar to ΔAMT.
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Solution:
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A(8, 9) = (x1, y1), B(1, 2) = (x2, y2) and P(6, 7) = (x, y)
Using Section formula of internal division,
∴ `7 = (m(square) - n(9))/(m + n)`
∴ 7m + 7n = `square` + 9n
∴ 7m – `square` = 9n – `square`
∴ `square` = 2n
∴ `m/n = square`
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