Is y = 2x - 4.9 a bisector of the line segment with endpoints at (-1.8 , 3.9) and (8.2 , -1.1)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The bisector of the line passing through (-1.8 , 3.9) and (8.2 , -1.1) would have to pass through their mid point.

Now the mid point of (-1.8 , 3.9) and (8.2 , -1.1) is

[(-1.8 + 8.2) / 2 , (3.9 -1.1) / 2]

=> (3.2 , 1.4)

Now if we substitute the x- coordinate in 2x - 4.9, we get 2*3.2 - 4.9 = 1.5

This is not equal to 1.4.

If the line y = 2x - 4.9, passed through (3.2 , 1.4), the y value we got would have been 1.4.

Therefore y = 2x - 4.9 is not a bisector of the line segment with endpoints at (-1.8 , 3.9) and (8.2 , -1.1)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'llĀ have to find the midpoint of the segment line, and then see if the midpoint is actually a point on the given line.

xM = (x1 + x2)/2

xM = (-1.8+8.2)/2

xM = 3.2

yM = (y1+y2)/2

yM = (3.9-1.1)/2

yM = 1.4

Now, we'll verify if the point is on the given line, substituting the coordinates of the midpoint in the eq. of the line.

yM = 2xM - 4.9

1.4 = 2*3.2 - 4.9

1.4 = 6.4 - 4.9

1.4 = 1.5

So, the given line is not the bisector of the segment whose endpoints are (-1.8,3.9) and (8.2,-1.1).

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