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The midpoint M of QR has coordinates (4, 5). Point R has coordinates (8, 5). Find the coordinates of point Q.

Write the coordinates as decimals or integers.
Q= ?

User Ryan Crews
by
8.3k points

2 Answers

3 votes

Answer :

  • (0,5)

Given :

  • Coordinates of Midpoint M = (4,5)
  • Coordinates of point R = (8,5)

Task :

  • To work out the co-ordinates of point Q

Solution :

We know that midpoint is given by ,


  • M = ((x_1 + x_2)/(2),(y_1 + y_2)/(2)) \\

wherein,

  • M = midpoint's coordinates
  • (x1,y1) = Coordinates of 1st point
  • (y1,y2) = coordinates of 2nd point

ATQ,

  • M = (4,5)
  • (x1,y1) = (8,5)

Thus,


  • (8 + x_2)/(2) = 4 \\ 8+ x_2 = 4 * 2 \\ x_2 = 8 - 8 \\ x_2 = 0 \\

  • (5 + y_2)/(2) = 5 \\ 5 + y_2 = 5 * 2 \\y_2 = 10 - 5 \\ y_2 = 5

Therefore, The co-ordinates of point Q are (0,5).

User Rob Osborne
by
8.7k points
3 votes

Answer:

Q = (0,5)

Explanation:

The midpoint of a segment is the point that is exactly halfway between the two endpoints of the segment. Therefore, the midpoint M of segment QR has the same y-coordinate as point R, which is 5.

To find the x-coordinate of point Q, we can use the midpoint formula:


\sf (x_M, y_M) =\left( (x_Q + x_R)/(2), (y_Q + y_R)/(2)\right)

Substituting in the known values, we get:


\sf (4,5) =\left( (x_Q+8)/(2), (y_Q+ 5)/(2)\right)

Let's solve x coordinate first.


\sf 4 = ( x_Q + 8)/(2)


\sf 4 \cdot 2 = x_Q + 8


\sf 8 = x_Q + 8


\sf x_Q = 8 - 8


\sf x_Q = 0

Now,

Let's solve y coordinate .


\sf 5 = ( y_Q + 5)/(2)


\sf 5 \cdot 2 = y_Q + 5


\sf 10 = y_Q + 5


\sf y_Q = 10 - 5


\sf y_Q = 5

Therefore, the coordinates of point Q are (0, 5).

User Ruben Danielyan
by
7.6k points

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