Question

if p ( 2, -3) is the midpoint of the line segment joining A (3,-10) and B (1,p) find p?​

Answer 1

Answer:

4

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Step-by-step explanation:

For any two points forming a straight line, the midpoint of the line is given by the Midpoint formula.

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$\dashrightarrow \sf \ M(x, y) = \Bigg\{ \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \Bigg\}$

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Where M(x, y) is the midpoint of the line formed on joining the points (x₁, y₁) and (x₂, y₂), and x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2.

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According to the question;

• Midpoint = P(2, -3)

• A = (3, -10)

• B = (1, p)

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On substituting these values in the Midpoint formula we get;

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$\dashrightarrow \sf \ M(x, y) = \Bigg\{ \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \Bigg\}$

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$\dashrightarrow \sf \ (2, -3) = \Bigg\{ \dfrac{3 + 1}{2} , \dfrac{-10 + p}{2} \Bigg\}$

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$\dashrightarrow \sf \ (2, -3) = \Bigg\{ \dfrac{4}{2} , \dfrac{-10 + p}{2} \Bigg\}$

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$\dashrightarrow \sf \ (2, -3) = \Bigg\{2 , \dfrac{-10 + p}{2} \Bigg\}$

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On equating -3 with (-10 + p)/2 we get; [Because y = (y₁ + y₂)/2]

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$\dashrightarrow \sf \ -3= \dfrac{-10 + p}{2}$

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$\dashrightarrow \sf -3 \times 2 = -10 + p$

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$\dashrightarrow \sf -6 = -10 + p$

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$\dashrightarrow \sf -6+ 10 = p$

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$\dashrightarrow \boxed{\sf 4 = p}$

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Therefore the value of 'p' is 4.