Question

If the mid point of the line segment Joining $\sf A {\bigg[}\dfrac{x}{2},\dfrac{y+1}{2}{\bigg]}$ and $\sf B(x+1,y-3)$ is $\sf C(5,-2)$, Find x and y

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Answer 1

Answer:

line segment has endpoints (0,4) and (5,6). What are the coordinates of the midpoint?

Possible Answers:

(2.5,-5)

(0,4)

(3,9)

(2.5,5)

(0,6)

Correct answer:

(2.5,5)

Explanation:

A line segment has endpoints (0,4) and (5,6). To find the midpoint, use the midpoint formula:

X: (x1+x2)/2 = (0+5)/2 = 2.5

Y: (y1+y2)/2 = (4+6)/2 = 5

The coordinates of the midpoint are (2.5,5).

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Find The Midpoint Of A Line Segment : Example Question #2

Find the midpoint between (-3,7) and (5,-9)

Possible Answers:

(4,-1)

(4,-8)

(-1,-1)

(1,-8)

(1,-1)

Correct answer:

(1,-1)

Explanation:

You can find the midpoint of each coordinate by averaging them. In other words, add the two x coordinates together and divide by 2 and add the two y coordinates together and divide by 2.

x-midpoint = (-3 + 5)/2 = 2/2 = 1

y-midpoint = (7 + -9)/2 = -2/2 = -1

(1,-1)

Step-by-step explanation:

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Answer 2

${\underbrace{\underline{\texttt{SOLUTION:-}}}}$

According to the question

C is the mid point of AB

Using mid point formula$\bf\bigg[\dfrac {x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg]$

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$\bf \therefore \dfrac{ \dfrac{x}{2}+( x+1)}{2} = 5$

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$\bf : \implies \dfrac{3x}{2}+1=10$

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$\bf:\implies \dfrac{3x}{2} = 10$

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$\boxed{\boxed{ \bf:\implies x = 6}} \longrightarrow \mathfrak{answer}$

And,

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$\bf \therefore \dfrac{ \dfrac{y + 1}{2} + (y - 3)}{2} = - 2$

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$\bf:\implies \dfrac{3y}{2} - \dfrac{5}{2} = - 4$

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$\bf:\implies \dfrac{3y}{2} = \dfrac{5}{2} - 4$

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$\bf:\implies \dfrac{3y}{2} = - \dfrac{3}{2}$

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$\boxed{ \boxed{ \bf : \implies y = - 1}} \longrightarrow \mathfrak{answer}$

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Hence the required value of x and y are 6 and -1 respectively.