A is the point (4,-3) and b is (-1,1). Find the gradient of a line perpendicular to AB. Plz help!!!!
slope of the line:
m=(-3-1)/(4+1)=-4/5
slope of the perpendicular (gradient)=5/4
use y=mx+c
now x1=4 and x2=-1
y1=-3 and y2=1
x1=4&y1=-3
sub into equation of the line
-3=m*4+c
4m+c=-3...(1)
now x2 and y2
1=-m+c
-m+c=1...(2)
subtract 2 from 1
5m=-3
m=-4/5
when perpendicular it is now 5/4
To find the gradient of a line perpendicular to AB, we first need to find the gradient of line AB, and then take the negative reciprocal of that gradient.
The gradient, also known as the slope, is calculated as the change in the y-coordinates divided by the change in the x-coordinates.
The coordinates of point A are (4, -3), and the coordinates of point B are (-1, 1). Therefore, the change in the y-coordinates is -3 - 1 = -4, and the change in the x-coordinates is 4 - (-1) = 5.
Now we can calculate the gradient of line AB by dividing the change in the y-coordinates by the change in the x-coordinates:
Gradient of AB = (-4) / 5 = -4/5
To find the gradient of a line perpendicular to AB, we take the negative reciprocal of this gradient. The negative reciprocal of a fraction is obtained by flipping the fraction and changing its sign.
The negative reciprocal of -4/5 is (5/4) with the sign flipped.
Therefore, the gradient of a line perpendicular to AB is 5/4.
It's important to note that the gradient of a line perpendicular to AB is the negative reciprocal because perpendicular lines have slopes that multiply to give -1.