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 answer is (2, 1)

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

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

$M = (2, 1)$

Answer 2

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

$\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).$

Therefore, according to the given information, we have

$\left(\dfrac{5+x}{2},\dfrac{2+y}{2}\right)=(-1,0)\\\\\\\Rightarrow \dfrac{5+x}{2}=-1\\\\\Rightarrow 5+x=-2\\\\\Rightarrow x=-2-5\\\\\Rightarrow x=-7$

and

$\dfrac{2+y}{2}=0\\\\\Rightarrow 2+y=0\\\\\Rightarrow y=-2.$

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