Question

The midpoint CD of is E(-1,0) . One endpoint isC (5, 2) .

What are the coordinates of the other endpoint?

Answer 1

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

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

We are to find the coordinates of the other endpoint D.

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

We know that the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) are given by

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

So, 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 other endpoint D are (-7, -2).

Answer 2

For this case we have that by definition, the midpoint formula is given by:

`(\frac {x_ {1} + x_ {2}} {2}, \frac {y_ {1} + y_ {2}} {2}) = (x_ {m}, y_ {m})`

We have to:

`(\frac {5 + x_ {2}} {2}, \frac {2 + y_ {2}} {2}) = (- 1,0)`

So:

`\frac {5 + x_ {2}} {2} = - 1\\5 + x_ {2} = - 2\\x_ {2} = - 2-5\\x_ {2} = - 7`

On the other hand:

`\frac {2 + y_ {2}} {2} = 0\\2 + y_ {2} = 0\\y_ {2} = - 2`

Finally we have to:

`D (-7, -2)`

Answer:

`D (-7, -2)`