Question

The midpoint of CD is E (-1,0). One endpoint is C (5,2). What are the coordinates of the other endpoint?

Answer 1

Answer: The required co-ordinates of the endpoint D are (-7, -2).

Step-by-step explanation: Given that the midpoint of CD is E (-1,0) and one endpoint is C (5,2).

We are to find the co-ordinates of the other endpoint D.

Let (x, y) represents the co-ordinates of the endpoint D.

We know that

the co-ordinates of the midpoint of a line segment withe endpoints (a, b) and (c, d) is given by

`\left((a+c)/(2),(b+d)/(2)\right).`

Therefore, according to the given information, we have

`\left((5+x)/(2),(2+y)/(2)\right)=(-1,0)\\\\\\\Rightarrow (5+x)/(2)=-1\\\\\Rightarrow 5+x=-2\\\\\Rightarrow x=-2-5\\\\\Rightarrow x=-7`

and

`(2+y)/(2)=0\\\\\Rightarrow 2+y=0\\\\\Rightarrow y=-2.`

Thus, the required co-ordinates of the endpoint D are (-7, -2).

Answer 2

The answer is (2, 1)

Step-by-step explanation

We can solve this by using midpoint formula

`M = (x_(1) + x_2)/2, (y_1 + y_2} ) /2`

because in a plane the coordinates of midpoint of a line is the average of each other coordinates.

So,

`x_1 = -1, x_2 = 5`

`y_1 = 0. y_2 = 2`

Putting values in formula as

`M = (-1+5) / 2, (0+2) / 2`

`M = (2, 1)`