The proof
Part I
Given the point A(2,7) and the line l1 with equation 3x – 4y – 8 = 0
1.
Find equation of the line AQ, which is perpendicular to l1 and passing through A.
2.
Find the coordinates of point Q, which is the point of intersection between the line AQ
and the line l1.
3.
Calculate the length of [AQ].
4.
On graph paper, plot the point A(2,7) and the line l1 with equation 3x – 4y – 8 = 0.
From point A, draw a perpendicular to the line l1. Let Q be the point of intersection
between the perpendicular and the line l1. From your graph, measure the length [AQ]
and compare it with the distance you previously calculated.
Part II
1.
Find a formula to calculate the perpendicular distance between the point ( x 1 , y1 ) and
the line ax  bx  c = 0, show that it reduces to:
ax1 + by1 + c
a2 + b2
Note
•
“The absolute value (or modulus) |a| of a real number a is a’s numerical value without
regard to its sign.”
[http://en.wikipedia.org/wiki/Absolute_value]
•
Use the formula above to calculate the length of [AQ] you previously measured and
calculated in Part I.