Question

what are the coordnates of D if E (-2,2)is the midpoint of DF and F has the coordnates of (3,5)

Answer 1

Hi there & welcome to brainly!

Answer:

( -7 , -1 )

Step-by-step explanation:

Let the co-ordinates of D be ( x , y )

Let D ( x , y ) be ( x1 , y1 ) and F ( 3 , 5 ) be ( x2 , y2 )

Midpoint of DF = E ( -2 , 2 )

Now, finding the co-ordinates of D :

$\boxed{\sf{ midpoint = (\frac{x1 + x2}{2} , \frac{y1 + y2}{2} ) }}$

⇒ $\sf{ ( - 2 , 2 ) = (\frac{x + 3}{2} , \frac{y + 5}{2} )}$

Equating corresponding elements, we get :

$\sf{-2 = \frac{x + 3}{2} }$                                  

⇒ $\sf{ -4 = x + 3 }$

⇒ $\sf{ x + 3 = -4 }$

⇒ $\sf{ x = -4 - 3}$

⇒ $\sf{x = -7 }$

Again,

$\sf{ 2 = \frac{y+5}{2} }$

⇒ $\sf{y + 5 = 4 }$

⇒ y = 4 - 5

⇒ y = -1

Hence, The co-ordinates of D = ( -7 , -1 )

Hope I helped!

Best regards! :D

~TheAnimeGirl