00:01
In this question, we are given with equation of line 3x plus 3y plus 3 equals to 0.
00:07
Now point on this line which is closest to the point minus 1 comma minus 5.
00:15
Now this can be represented as this.
00:17
This is the required point on line with x y coordinates and this is a minus 5 comma minus 1.
00:25
And equation of this line is 3x plus 3y plus 3 equals to 0.
00:31
So if we find equation of this line, so point of intersection of these two lines will give the closest point.
00:39
Now slope of the given line 3x plus 3y plus 3 equals to 0.
00:46
So this can be written as dividing the whole equation by 3.
00:51
So x plus y plus 1 equals to 0.
00:54
So this implies y is equals to minus x minus 1.
01:00
So coefficient on comparing with on comparing this equation with y equals to mx plus c.
01:13
So from here slope of the line is minus 1.
01:17
So if two lines are perpendicular, if two lines are perpendicular, therefore they are product of slope m1 into m2 equals to minus 1.
01:34
So this implies m2 equals to minus 1 upon m1.
01:39
So this is minus 1 upon minus 1.
01:43
This is 1.
01:44
So here this represents line 1 and this represents line 2 and both are perpendicular.
01:51
So its slope is m1 which is minus 1 and its slope is m2 which is plus 1...