Question

ABC is a triangle in which A(0,2) and B(4,0).if (4,4) is the midpoint of of bc then the midpoint of AC is

Answer 1

Step-by-step explanation:

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Answer 2

The midpoint of AC is ( 2, 5 ).

Given: ABC is a triangle in which A(0,2) and B(4,0). (4,4) is the midpoint of BC.

To Find: The midpoint of AC.

Solution:

• The midpoint of two points A( x1, y1 ) and B( x2, y2 ) can be found by the formula,

        Midpoint M ≡ ( ( x1 + x2 )/2 , ( y1 + y2 )/2 )                      .....(1)

Coming to the numerical, we are given;

     A( 0, 2 ) and B( 4, 0 )

Also, the midpoint of BC is ( 4, 4 ).

Let us take the coordinates of C to be (x,y).

So according to (1), we can say that;

    Midpoint M ≡ ( ( x1 + x2 )/2 , ( y1 + y2 )/2 )    

⇒   Midpoint of BC ≡ ( ( 4 + x )/2 , ( y + 0 )/2 )

⇒   ( 4, 4 )  ≡ ( ( 4 + x )/2 , y /2 )

∴ ( 4 + x )/2 = 4 ⇒ x = 4

∴   y / 2 = 4 ⇒ y = 8

∴ Coordinates of C are ( 4, 8 ).

Now, we need to find the midpoint of AC, So again using (1), we get

      Midpoint M ≡ ( ( x1 + x2 )/2 , ( y1 + y2 )/2 )

 We know that A ( 0, 2 ) and C ( 4, 8 ), so putting respective values,

  ⇒ M ≡ ( ( 0 + 4 )/2 , ( 2 + 8 )/2 )

  ⇒ M ≡ ( 2, 5 )

Hence, the midpoint of AC is ( 2, 5 ).

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