Determine the ratio and the value of m in which the point P(m, 6) divides the…
2019
Determine the ratio and the value of m in which the point P(m, 6) divides the join of A(−4, 3) and B(2, 8).
- A.
3 : 4 and m = −2/5
- B.
3 : 4 and m = 2/5
- C.
3 : 2 and m = −2/5
- D.
3 : 2 and m = 2/5
Attempted by 55 students.
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Correct answer: C
Method: use the section formula.
Let AP:PB = k:1. Use the y-coordinate of P: (8k + 3)/(k + 1) = 6.
Solve for k: 8k + 3 = 6(k + 1) ⇒ 8k + 3 = 6k + 6 ⇒ 2k = 3 ⇒ k = 3/2. So the ratio is 3 : 2.
Find m from the x-coordinate: x = (2k − 4)/(k + 1). Substitute k = 3/2: x = (2*(3/2) − 4)/(3/2 + 1) = (3 − 4)/(5/2) = −1/(5/2) = −2/5. Thus m = −2/5.
Answer: P divides AB in the ratio 3 : 2, and m = −2/5.
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