Given the points A(1,8), B(4,7) and O(0,0). Find the equation of the line though B perpendicular to AB?

First, we need to find the slope of line AB:

Slope of AB = (y2 - y1) / (x2 - x1)
Slope of AB = (7 - 8) / (4 - 1)
Slope of AB = -1 / 3

The slope of a line perpendicular to AB will be the negative reciprocal of the slope of AB. So, the slope of the line perpendicular to AB is 3.

Now, we have the slope of the line perpendicular to AB and a point on the line (B). We can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1)
y - 7 = 3(x - 4)
y - 7 = 3x - 12
y = 3x - 5

Therefore, the equation of the line through B perpendicular to AB is y = 3x - 5.

Step 1: Find the slope of line AB

Slope (m) = (y2-y1)/(x2-x1)
= (7-8)/(4-1)
= -1/3

Step 2: Find the slope of the line perpendicular to AB

The slope of a line perpendicular to another is the negative reciprocal.

Slope (m') = -1/(-1/3)
= 3

Step 3: Use the point-slope form to find the equation of the line

Point-slope form: y - y1 = m(x - x1)

Using point B(4,7) and slope m' = 3

y - 7 = 3(x - 4)

Step 4: Simplify the equation to slope-intercept form

y - 7 = 3x - 12
y = 3x - 5

Therefore, the equation of the line through B perpendicular to AB is y = 3x - 5.