00:01
Hello students, let's solve each problem step by step.
00:03
The first one is finding an equation which passes through 8 -2 and y intercepts i .e.
00:09
8 -2 and 0, 5.
00:12
To find the equation of line, we need to use the midpoint slope form of the equation of line i .e.
00:17
Y -y1 is equal to m into x -x1.
00:21
Since where x1 and y1 is the given point and m is the slope of the line, since the line passes through 8 -2 and has y intercept equal to 5, it means 0 line passes through 0, 5.
00:34
So let's find that m is equal to minus 2 minus 5 by 8 minus 0 that is equal to minus 7 by 8.
00:43
Now we can use the point slope form with the point 8 minus 2.
00:46
So y minus of minus 2 is equal to minus 7 by 8 into x minus 8.
00:52
Simplifying this, we will have y plus 2 equal to minus 7 by 8 into x minus 8.
01:01
Now moving forward to the second bit, find an equation of the line which passes through 1, 4 and minus 3, 2.
01:09
M is equal to 2 minus 4 by minus 3 minus 1 that is equal to minus 2 by minus 4.
01:18
This is equal to 1 by 2.
01:19
Using this point 1, 4, we can say y minus 4 equal to 1 by 2 x minus 1.
01:27
So simplifying we have y equal to 1 by 2 x plus 2 .5.
01:36
Now the third bit, to find an equation of the line passing through the point 5, 7 and 5 minus 8, this line passes through the two points with the same x -coordinate which means the line is vertical and its equation will be on the form x is equal to c, where c is the x -coordinate of the point passes through.
01:56
In this case, the equation of the line is x is equal to 5.
02:00
So our answer is x is equal to 5.
02:04
Now moving forward to the fourth bit, finding an equation of the line that passes through the point 4 minus 8 and is perpendicular to the line 2x, 2x minus 5y is equal to 20.
02:20
To find the equation of the perpendicular line, we need to find the slope first.
02:25
The slope of the given line is 2x minus 5y equal to 20.
02:31
So minus 5y equal to minus 2x plus 20 and y is equal to 2 by 5 x minus 4.
02:41
The slope of the line is 2 by 5.
02:43
For the perpendicular line, the slope will be the negative reciprocal of 2 by 5 which is perpendicular line, slope is equal to minus 5 by 2.
02:56
Now using the point slope form, the point 4 minus 8 that is y minus, minus 8 is equal to minus 5 by 2 into x minus 4.
03:05
So y plus 8 equal to y equal to minus 5 by 2 x plus 2.
03:14
So our answer is y equal to minus 5 by 2 x plus c.
03:19
Now the fifth bit, to find an equation of the perpendicular bisector of the line segment between the 6, 6 minus 3 and 2, 5, the perpendicular bisector of the line segment is a line that passes through the midpoint of the segment and is perpendicular to it.
03:36
To find the equation, we need to find the midpoint...