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What is the midpoint of the line segment with endpoints (-2,-2) and (4, 6)?

User Ctc
by
8.4k points

2 Answers

5 votes

Answer:

(1,2)

Explanation:

(x,y) = ((x1+x2)/2 , (y1+y2)/2)

[substitute values given]

(x,y) = ((-2+4)/2 , (-2+6)/2)

[solve the equation]

(x,y) = (2/2 , 4/2)

[simplify the values]

(x,y) = (1 , 2)

User Vanao Veneri
by
8.1k points
7 votes

Let's solve ~

We can use section formula to find the mid - point of the given line segment as it divied the line segment into ratio of 1 : 1

Let the coordinates of mid - point be (x , y)


\qquad \sf  \dashrightarrow \: x = (mx_2 - nx_1)/(m + n)


\qquad \sf  \dashrightarrow \: y= (my_2 - ny_1)/(m + n)

here,


  • \sf{x_1 = -2 }


  • \sf{y_1 = -2 }


  • \sf{x_2 = 4 }


  • \sf{y_2 = 6}

The ratio is m : n ~ i.e equivalent to 1 : 1, meaning m = n = 1.


\qquad \sf  \dashrightarrow \: x = (4 - ( - 2))/(1 + 1)


\qquad \sf  \dashrightarrow \: x = (4 + 2)/(2)


\qquad \sf  \dashrightarrow \: x = (6)/(2)


\qquad \sf  \dashrightarrow \: x = 3

similarly ~


\qquad \sf  \dashrightarrow \: y= (6 - ( - 2))/(1 + 1)


\qquad \sf  \dashrightarrow \: y= (6 + 2)/(2)


\qquad \sf  \dashrightarrow \: y= (8)/(2)


\qquad \sf  \dashrightarrow \: y = 4

So, the midpoint of the line segment has coordinates:

  • (3 , 4)
User SpellTheif
by
8.3k points

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