ANALYTIC GEOMETRY
1. Find the slope of the line through the points (—2, 5) and (7,1)
2. Find a point-slope equation of the line through the points (1, 3) and (3, 6)
3. Write a point-slope equation of the line through the points (1,2) and (1,3).
4. Find a point-slope equation of the line going through the point (1,3) with slope 5.
5. Find the slope-intercept equation of the line through the points (2,4) and (4,8).
11. Determine k so that the points A (7,5), B (-l, 2), and C (k, 0) are the vertices of a right triangle with
right angle at B.
Solution:
Let: m1 = AB
Let: m2 = BC
m2 = (2 – 0) / (-1 - k) = - 2 / (1+k)
Note: Right triangle to have right angle at B, line AB and BC are perpendicular when the product of its
slope is equal to -1.
Use shift calc function to solve k.
Therefore, k = - 0.25 or -1/4
12. Find the slope-intercept equation of the line through (1,4) and rising 5 units for each unit increase in
x.
Solution:
Since the line rises 5 units for each unit increase in x, its slope must be 5.
y = 5x + b
b = 4 – 5(1) = -1
Therefore, y = 5x - 1
14. Find the midpoint of the line segment between (2, 5) and (—1, 3).
Calculator Technique:
Add X and Y value to Point (2, 5)
X = 2 + (-1.5) = 1/2
Y = 5 + (-1) = 4
Manual solution is faster compared to Calculator Technique in finding midpoints or coordinates of a
points that bisect the line.
15. Find the intersection of the line L through (1, 2) and (5, 8) with the line M through (2,2) and (4, 0).
Solution: (Note: To solve this problem find the slope of L and M then plug the value to slope-intercept
form to calculate the y-intercept b. Next, find the point of intersection (x, y).
Slope of L: (Recall the calculator technique to find the slope).
Slope of M:
Hence, m1 = 3/2 and m2 = -1
Slope-intercept equation of L: @Point (1, 2)
y = 3/2x + b
b = 2 – 3/2(1) = 1/2
Complete the slope-intercept equation in the form of Ax + By = 0
3/2x – y = -1/2
Eq.1
Slope-intercept equation of M: @Point (2, 2)
y = -x + b
b=2+2=4
x+y=4
Eq.2
Evaluate 2 equations 2 unknowns using Calculator Technique Mode 5, 1
Therefore, the intersection of the line L and line M is (7/5, 13/5)