For this case we have that by definition, the midpoint formula is given by:
[tex](\frac {x_ {1} + x_ {2}} {2}, \frac {y_ {1} + y_ {2}} {2}) = (x_ {m}, y_ {m})[/tex]
We have to:
[tex](\frac {5 + x_ {2}} {2}, \frac {2 + y_ {2}} {2}) = (- 1,0)[/tex]
So:
[tex]\frac {5 + x_ {2}} {2} = - 1\\5 + x_ {2} = - 2\\x_ {2} = - 2-5\\x_ {2} = - 7[/tex]
On the other hand:
[tex]\frac {2 + y_ {2}} {2} = 0\\2 + y_ {2} = 0\\y_ {2} = - 2[/tex]
Finally we have to:
[tex]D (-7, -2)[/tex]
Answer:
[tex]D (-7, -2)[/tex]
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
[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
So, according to the given information, we have
[tex]\left(\dfrac{5+x}{2},\dfrac{2+y}{2}\right)=(-1,0)\\\\\\\Rightarrow \dfrac{5+x}{2}=-1\\\\\Rightarrow 5+x=-2\\\\\Rightarrow x=-2-5\\\\\Rightarrow x=-7[/tex]
and
[tex]\dfrac{2+y}{2}=0\\\\\Rightarrow 2+y=0\\\\\Rightarrow y=-2.[/tex]
Thus, the required co-ordinates of the other endpoint D are (-7, -2).
