Question

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= ?

Answer 1

• (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).

Answer 2

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).