Answer:
a. Gradient of line AB is
b. The gradient of a line perpendicular to line AB is 3
c. The equation of a line passing through point (4,2) and perpendicular to AB is
Step-by-step explanation:
a.
Given
Point A (1, 3) B (7, 1)
Required
Gradient of AB
Gradient of a line is represented by m
m is calculated using the following formula
Where the general representation of the coordinates are
<em>From the given data, we have that</em>
<em>So, from there we know that</em>
becomes
b.
Required
Find the gradient of a line perpendicular to AB
<em>Recall that gradient of a line is represented by m</em>
The condition for perpendicularity is that
In (a) above, we solved the gradient of line AB to be
Let represent gradient of line AB
Hence,
Substitute for
in
<em>This will give</em>
Multiply both sides by -3
Hence, the gradient of a line perpendicular to line AB is 3
c.
Required
Find the equation of a line passing through point (4,2) and perpendicular to AB
Equation is calculated using the gradient formula
Since only one point is known, the formula is represented as follows
Where
Since, the line is perpendicular to line AB, then its gradient m is equal to 3 (as calculated in b above)
So, we have
By substitution
becomes
Multiply both sides by x - 4
Open brackets
Make y the subject of formula
Reorder
Hence, the equation of a line passing through point (4,2) and perpendicular to AB is