Question

The coordinates of point T are ​(​0,6​). The midpoint of is ​(​6,-2​). Find the coordinates of point S.

Answer 1

To find the coordinates of point S, you can use the midpoint formula, which calculates the midpoint between two points. The midpoint formula is:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

In this case, you have the midpoint, which is (6, -2), and one of the points, which is T(0, 6).

So, plug these values into the formula:

Midpoint = ((x1 + 0) / 2, (y1 + 6) / 2)

Simplifying:

Midpoint = (x1 / 2, (y1 + 6) / 2)

Now, you have the coordinates of the midpoint (6, -2), so you can set up the equations:

6 = x1 / 2 (for the x-coordinate)

-2 = (y1 + 6) / 2 (for the y-coordinate)

Let's solve for x1 and y1:

For x1:

6 = x1 / 2

x1 = 6 * 2

x1 = 12

For y1:

-2 = (y1 + 6) / 2

-2 * 2 = y1 + 6

-4 = y1 + 6

y1 = -4 - 6

y1 = -10

So, the coordinates of point S are (12, -10).

Answer 2

(12,-10)

Explanation:

The midpoint of a segment with endpoints is given by the formula:

`\sf m(x,y)= \left((x_1 + x_2)/(2), (y_1 + y_2)/(2)\right)`

In this case, the midpoint is given as (6, -2).

So, we have the following equations:

`\sf (x_1 + x_2)/(2 )= 6`

`\sf (y_1 + y_2)/(2) = -2`

Over here,

`\sf x_1= 0 and y_1=6`

Substitute the value given value in first equation and solve:

we get

`\sf (0+ x_2)/(2 )= 6`

`\sf x_2=6* 2`

`\sf x_2=12`

Similarly:

`\sf (6 + y_2)/(2) = -2`

`\sf 6+y_2=-2* 2`

`\sf y_2 = -4-6`

`\sf y_2=-10`

Therefore, coordinate of point S is (12,-10)