MMW Midterm Practice Examination
While this is not graded, solve the following to help you prepare for the actual exam. Allow yourself to
solve all of them for two hours. The solutions will be given tomorrow afternoon/evening.
1. Determine the equation of a line that is perpendicular to 4๐ฅ โ 3๐ฆ = 5 and passes through (4,2).
2. Find the slope of a line that passes through points (-2, -8) and (3, 10).
3. Write the equation of a line that has a slope of -3 and passes through the point (-2, 4).
4. Find the equation of the line that passes through points (1, 2) and (-3, 6).
5. What is the area of the triangle that has vertices (3, -6), (-4, -8), and (2, 1)?
6. One line passes through points (1, 9) and (2, 6). Another line passes through (3, 3) and (1, -5).
What is the acute angle between the two lines?
7. What is the area of the triangle that has vertices (-3, 2), (3, 6), and (0, -4)?
8. What is the equation of the line that is perpendicular to 11x โ 3y = 5 and passes through (1, 5)?
9. What is the equation of the line that is parallel to -2x + 13y = 0 and passes through (-2,10)?
10. Find the equation of the line that has a slope of -2 and a y-intercept of 9.
11. What is the equation of the line that is parallel to โ13๐ฅ โ ๐ฆ = 0 and passes through (1
5,4)?
12. What is the equation of the line that is perpendicular to โ13๐ฅ โ ๐ฆ = 10 and passes through
(1
5,4)?
13. Find the distance between two parallel lines 4๐ฅ + 15 = ๐ฆ;12๐ฅ โ 3๐ฆ = 6.
14. Given the line equation โ15
4๐ฅ โ 3
7๐ฆ = 6, find the following
a. x-intercept
b. y-intercept
c. Slope of the line
d. The equation of the parallel line that passes through point (20, 4)
e. From your answer in (d), find the distance of the two parallel lines from each other.
f. The distance of point (-5, 2) from the line equation (14).
g. The distance of point (-5, 2) from the line equation (d).
15. Determine location of the trigonometric identities that have negative signs in the Cartesian
Coordinate Plane.
16. Find the acute and obtuse angle of the lines 4๐ฅ + ๐ฆ = 7;3๐ฅ โ 2๐ฆ = 0.
17. Given the line equation โ17
4๐ฅ โ 14
โ17 ๐ฆ = 15, find the following
a. x-intercept
b. y-intercept
c. Slope of the line
d. The equation of the parallel line that passes through point (-5, 0)
e. The equation of the perpendicular line that passes through point (-5, 0)
f. The equation of the parallel line that passes through point (-5, 4)
g. The equation of the perpendicular line that passes through point (-5, 4)
h. From your answer in (d), find the distance of the two parallel lines from each other.
i. From your answer in (f), find the distance of the two parallel lines from each other.
j. The distance of point (-8, 11) from the line equation (17).
k. The distance of point (-8, 11) from the line equation (d).
l. The distance of point (-8, 11) from the line equation (f).
m. The distance of point (-8, 11) from the line equation (g).
