The answer is (2, 1)
We can solve this by using midpoint formula
[tex]M = (x_{1} + x_2)/2, (y_1 + y_2} ) /2[/tex]
because in a plane the coordinates of midpoint of a line is the average of each other coordinates.
So,
[tex]x_1 = -1, x_2 = 5[/tex]
[tex]y_1 = 0. y_2 = 2[/tex]
Putting values in formula as
[tex]M = (-1+5) / 2, (0+2) / 2[/tex]
[tex]M = (2, 1)[/tex]
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
[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Therefore, 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 endpoint D are (-7, -2).
