Question

The equation of line is y = x. The midpoint of BC is (a + c, b). Does the midpoint of BC lie on ? Why or why not? no, because b does not equal a + c no, because (a + c) does not equal b yes, because b = a + c yes, because (a + c) = b

Answer 1

yes because (a + c) = b

Explanation:

Answer 2

yes, because (a+c) =b

Explanation:

Given that equation of the line is y=x.

B and C are two points lying on this line.

Midpoint of B and C are given as (a+c, b)

From this we see that using midpoint formula

`a+c=(x1+x2)/(2 ) and\\b=(y1+y2)/(2 )`

Since both points lie on y=x, we get

x1=y1 and x2=y2

So x1 = a+c and 2y1 = 2b or y1 =b

Since x1=y1, we have a+c =b

i.e. the coordinates of mid point satisfy the equation y=x

Hence answer is

yes, because (a+c) =b