Write the equation of the perpendicular bisector of bc.

 The equation of the perpendicular bisector of a line segment can be found using the midpoint and slope of the line segment.

To find the equation of the perpendicular bisector of line segment BC, first find the midpoint of the segment by averaging the x-coordinates and y-coordinates of the two endpoints.

The midpoint is the point (x1+x2)/2,(y1+y2)/2

Then, find the slope of the line segment by using the formula (y2-y1)/(x2-x1)

The slope of the line that is perpendicular to the line segment is the negative reciprocal of the slope of the line segment.

To find the equation of the line, you can use the slope-intercept form of a line, y = mx + b, where m is the slope, and b is the y-intercept.

The y-intercept can be found by substituting the midpoint coordinates and the slope into the equation, and solving for b.

The equation of the perpendicular bisector of line segment BC is y = -(1/(m))*x + (y-mx)

It is recommended to substitute the value of point B and point C, and then find the equation of the line.

Write the equation of the perpendicular bisector of bc step by step guide.

Find the midpoint of line segment BC. You can do this by averaging the x-coordinates and y-coordinates of points B and C. For example, if B is at (x1, y1) and C is at (x2, y2), the midpoint M is at ((x1 + x2)/2, (y1 + y2)/2).

Now, you will use the midpoint M to find the slope of the line that is perpendicular to BC. Since the line is perpendicular, the slope will be the negative reciprocal of the slope of line BC.

The slope of line BC is (y2-y1)/(x2-x1) so the slope of the line perpendicular to it will be -(x2-x1)/(y2-y1)

Now that you have the slope, you can use the point-slope form of a line which is y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line.

Substitute the coordinates of the midpoint you found in step 1 for (x1, y1) and the slope you found in step 2 for m.

Now you have the equation of the line that contains the perpendicular bisector of BC

The final equation of the Perpendicular bisector will be in the form of y-y1 = -(x2-x1)/(y2-y1)(x-x1)

The equation of the perpendicular bisector of a line segment can be found by first finding the midpoint of the line segment and the slope of the line that is perpendicular to the original line.

In order to write the equation of the perpendicular bisector of BC, you would need to know the coordinates of the two endpoints of the line segment, B(x1, y1) and C(x2, y2).

Once you have the coordinates, the midpoint of the line segment can be found using the formula:

M(x,y) = ((x1+x2)/2 , (y1+y2)/2)

The slope of the perpendicular bisector can be found using the negative reciprocal of the slope of the line segment BC which is (y2 - y1) / (x2 - x1)

With the slope and the midpoint you can find the equation of the line.

y - (y1+y2)/2 = -(x2-x1)/(y2-y1) * (x - (x1+x2)/2)

So the equation of the perpendicular bisector of BC is y = -(x2-x1)/(y2-y1) * x + (y1+y2)/2 + (x1+x2)/(y2-y1)

Conclusion:

The equation of the perpendicular bisector of a line segment can be found by using the coordinates of the endpoints of the line segment, the midpoint formula and the slope formula.