Indicate the equation of the given line in standard form. the line that is the perpendicular bisector of the segment whose endpoints are r(-1, 6) and s(5, 5)

Step-by-step explanation:

We are given that a line that is perpendicular bisector of  the line whose end points are R(-1,6) and S(5,5).

To find the equation of perpendicular line then we have find the slope of line and a point through which perpendicular line is  passing .

To find the point through which perpendicular line is passing then we have find the mid point of the line joining points R(-1,6) and S(5,5)

Mid point formula: The coordinates of mid point

Let P is the mid point of the line joining the points R (-1,6) and S(5,5)

Therefore, the coordinates of mid point P by using mid point formula

The coordinates of mid point P of the line joining points  R and S

Slope of line RS,

Slope of line RS,

Slope of perpendicular line is opposite reciprocal of the line RS

Hence, the slope of perpendicular line

Slope of perpendicular line,

The perpendicular line is passing through the mid point P because it bisect the line RS at mid point P.

The equation of perpendicular line passing through the point P with slope 6

The equation of a line which is perpendicular to RS

The equation of  line which is perpendicular to the line RS is given by

The  equation of a line which is  perpendicular to the  line RS

Hence, the required equation of a line which is perpendicular to the line RS