The ratio in which (4,5) divides the join of (2,3) and (7,8) is ________
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Answer:
- 2 : 3 is the required ratio.
Step-by-step explanation:
Let the ratio be m_1 and m_2.
Using section formula:
[m_1x_2 + m_2x_1/m_1 + m_2],[m_1y_2 + m_2y_1/m_1 + m_2]
We have points:
› A(2,3) and B(7,8).
Substituting:
› [m_1(7) + m_2(2)]/m_1 + m_2,[m_1(8) + m_2(3)/m_1 + m_2]
⇒ 4 = [m_1(7) + m_2(2)]/m_1 + m_2
⇒ 4(m_1 + m_2) = 7m_1 + 2m_2
⇒ 4m_1 + 4m_2 = 7m_1 + 2m_2
⇒ 4m_1 - 7m_1 = 2m_2 - 4m_2
⇒ -3m_1 = -2m_2
⇒ 3m_1 = 2m_2
⇒ m_1/m_2 = 2/3
or,
⇒ 5 = [m_1(8) + m_2(3)/m_1 + m_2]
⇒ 5 = 8m_1 + 3m_2/m_1 + m_2
⇒ 5(m_1 + m_2) = 8m_1 + 3m_2
⇒ 5m_1 + 5m_2 = 8m_1 + 3m_2
⇒ 5m_1 - 8m_1 = 3m_2 - 5m_2
⇒ -3m_1 = -2m_2
⇒ 3m_1 = 2m_2
⇒ m_1/m_2 = 2/3
∴ The required ratio is 2:3.
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