1. Refer to the given coordinate grid below.
a) Find the distance between L and N
b) Find the coordinates of the midpoint of ̅̅̅̅̅
𝑀𝑁 algebraically. Show complete working.
c) Find the coordinates (algebraically) of a point Q if P is the midpoint of ̅̅̅̅
𝑁𝑄 . Show
complete working.
̅̅̅̅ and passes through point P. Write the
d) Find the equation of line parallel to 𝐿𝑀
equation in both point-slope form and slope-intercept form.
e) Graph the equation of the line in part d on the grid. Clearly label three points on the
line.
3
2. A line segment with endpoint 𝐴(4, −3) and𝐵(−6, 𝑘) has a slope of − 5
a) Find the value of 𝑘 .
̅̅̅̅. Write the equation in the
b) Find the equation of the perpendicular bisector to 𝐴𝐵
form 𝑎𝑥 + 𝑏𝑦 = 𝑐 where 𝑎 > 0.
3. Two points 𝑋(3𝑚 − 1, 2𝑚 + 5) and 𝑌(−𝑚 + 6, 4𝑚 − 3) are on the same line that is
2
perpendicular to the equation 𝑦 = − 3 𝑥 + 5. Find the value of 𝑚.
1. Solve the following system of equations using an appropriate algebraic method.
a)
−3𝑥 + 4𝑦 = 6
6𝑥 − 8𝑦 = −12
b)
2𝑥 − 4𝑦 = 10
6𝑥 − 12𝑦 = 20
c)
4𝑥 − 2𝑦 = 4
5𝑥 + 3𝑦 = 16
2. If twice the age of son is added to age of father, the sum is 56. But if twice the age of the
father is added to the age of son, the sum is 82.
a) Set up a system of equations that represents the situation above. Make sure to write
“let” statements to declare or define the variables you plan on using.
b) Using an appropriate algebraic method, Find the ages of father and son.
3. The perimeter of the rectangle is 158 cm. If the length is 7 more than 3 times the width.
a) Set up a system of equations that represents the situation above. Make sure to write
“let” statements to declare or define the variables you plan on using.
b) Using an appropriate algebraic method, Find the area of rectangle.
4. Solve each inequality and graph its solution on the given number line.
a) 6 −
2(𝑝−1)
3
> −6
b) 2𝑥 − 6 < −4
OR 3𝑝 −
𝑝−9
3
AND 1 − 𝑥 ≥ 9
>0
c) 3𝑥 − 2(𝑥 − 2) < −1 AND
2
𝑥
3
− 1 > −3
5.
a) Sketch the solutions to the system of inequalities on the axes provided below. Make
sure to label each boundary line clearly with at least points per line.
2𝑥 − 𝑦 < −3
𝑥 − 3𝑦 ≥ 6
𝑦 < −1
b) A perpendicular line passes through the 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 of the steepest line in part
(a) above. Write the equation of this perpendicular line in slope-intercept form.
6. Write a system that following the shaded region as it’s solution.
7.
Use the graph to solve the inequality.
1
a. 2|𝑥 − 3| + 1 = − 2 |𝑥 − 3| + 6
1
2
b. 2|𝑥 − 3| + 1 ≥ − |𝑥 − 3| + 6
1
c. 2|𝑥 − 3| + 1 ≤ − 2 |𝑥 − 3| + 6
8.
Use the graph to solve the inequality.
a. 2|𝑥 − 1| − 1 = −|𝑥 − 3|
b. 2|𝑥 − 1| − 1 > −|𝑥 − 3|
c. 2|𝑥 − 1| − 1 < −|𝑥 − 3|
9. Solve
a.
b.
c.
d. 2|𝑥 − 1| − 4 ≤ 2
e.
f.