NAME: ______
DAY 1 - DO NOW: REVIEW
1)What are the coordinates of (-4, -2) after ?
2)What is the measure of a vertex angle of an isosceles triangle if each base angle is 74°?
3)Algebra review: What does the word undefined mean?
LESSON – SLOPE FORMULA
What is the slope formula?
Practice Exercises:
1)What is the slope between A(2, 3) and B(5, 9)?
2)What is the slope between C(-4, 4) and D(-1, -3)?
3)What is the slope between E(-3, -6) and F(5, -2)?
4)What is the slope between G(1, 8) and H(7, 8)?
5)What is the slope between I(-3, 4) and J(-3, 0)?
6)Find the slope of AB and CD, and determine the relationship between the two lines. Justify your answer.
A(2, 0), B(5, 8)C(5, -3), (8, 5)
7)Find the slope of EF and GH, and determine the relationship between the two lines. Justify your answer.
E(-3, 7), F(1, 0)G(-4, 1), H(3, 5)
HOMEWORK: Page 295, #3-11 part B only
DAY 2 - DO NOW: REVIEW
1)What are the coordinates of (6, -5) after ?
2)What is the converse of “If I go shopping, then I do not save money?”
3)Algebra review: Simplify the following radical:
LESSON – DISTANCE FORMULA
Today, we are going to use basic examples to discover the distance formula ourselves.
1)What is the distance between (1, 3) and (4, 3)?
2)What is the distance between (4, 3) and (4, 7)?
3)Now, how can we determine the distance between (1, 3) and (4, 7) using a math concept from
algebra? Also, using that concept, what is the distance between these two points?
**Utilizing the concept from exercise #3, let’s now discover the distance formula**
Let’s apply our distance formula now into some practice exercises.
4)What is the distance between (-3, 4) and (5, -2)?
5)A) What is the distance, in radical form, between (0, -1) and (5, -7)?
B) What is the distance of exercise #5A if the directions said to round to the nearest tenth?
6)What is the lengthof the line segment connecting (-3, -1) and (-1, 3), in simplest radical form?
7)Use the distance formula to determine if AB is congruent to CD. Explain your answer.
A(3, 2), B(5, -1)C(0, 0), D(-3, 4)
8)Use the distance formula to determine if EF is congruent to GH. Explain your answer.
E(6, -2), F(-1, -1)G(2, 3), H(3, 10)
HOMEWORK: Page 525, #3-10
DAY 3 – DO NOW: REVIEW
1)What are the coordinates of (5, -5) after ?
2)What is the slope between the coordinates (8, 7) and (4, 2)?
3)Algebra Review: What is the mean of the numbers 6 and 18?
LESSON – MIDPOINT FORMULA
Just like the distance formula, we are going to use basic examples to discover the midpoint formula ourselves.
1)What is the midpoint between the coordinates (2, 1) and (2, 7)?
2)What is the midpoint between the coordinates (8, -4) and (1, -4)?
Now, what happens when we need to find the midpoint of a diagonal line?
3)What is the midpoint between the coordinates (-3, 5) and (-5, 1)?
**Utilizing the concept from the previous exercises, let’s now discover the midpoint formula**
Let’s apply our midpoint formula now into some practice exercises.
4)The coordinates of A are (-6, 4) and the coordinates of B are (2, 8). Using the midpoint formula, what are the coordinates of the midpoint of AB?
5)The coordinates of C are(7, 8) and the coordinates of D are (2, 3). Using the midpoint formula, what are the coordinates of the midpoint of CD?
How do we approach an exercise where they give us an endpoint and the midpoint, and we are asked for the other endpoint? This is a common concept asked on the Regents!
6)The coordinates of E are (5, 0) and the coordinates of M, the midpoint of EF, are (5, 4). What are the coordinates of F?
7)The midpoint of GH has the coordinates (-2, 1) and the coordinates of G are (-4, 5). What are the coordinates of H?
8)The coordinates of P are (1, 6) and the coordinates of M, the midpoint of PQ, are
(-3, 1.5). What are the coordinates of Q?
9)Use the midpoint formula to determine if AB and CD bisect each other. Explain your answer.
A(2, 4), B(8, 9)C(1, 7), D(9, 6)
10)Use the midpoint formula to determine if EF and GH bisect each other. Explain your answer.
E(-5, 8), F(0, 2)G(-6, -1), H(-1, 5)
HOMEWORK: #3-19 odd
DAY 4 – DO NOW: REVIEW
1)What is the inverse of “If the sky is blue, then it is not raining?”
2)What are the coordinates of A’, the image of A(5, 7), after a reflection in the line x = 4?
3)Algebra Review – In the linear equation y = 3x – 8, what does the 3 represent, and what does the -8 represent?
LESSON – EQUATIONS OF LINES
What is the general formula for the equation of a line, and what do the letters represent?
Now, let’s use that concept in a variety of examples.
1)What is the equation of a line with a slope = 2 that goes through the point (-3, 4)?
2)What is the equation of a line with a slope = -3 that goes through the point (-2, -1)?
3)What is the equation of a line with a slope = that goes through the point (8,0)?
4)What is the equation of a line that goes through the points (3, 2) and (4, 6)?
5)What is the equation of a line that goes through the points (-4, 1) and (4, -1)?
6)What is the slope and y-intercept of the line whose equation is 5y = 20x – 15?
7)What is the slope and y-intercept of the line whose equation is 2y – 6 = -3x?
8)What is the slope and y-intercept of the line whose equation is 3y + 3x = 21?
Homework: Page 299, #3-14
DAY 5 – DO NOW: REVIEW
1)What is the distance between the coordinates (4, 2) and (2, -4) in simplest radical form?
2)What is the midpoint between the coordinates (-6, -3) and (-2, 0)?
3)What is the slope and y-intercept of the line 4y = x – 24?
LESSON – SLOPES OF PARALLEL LINES
**Let’s look back at Day 1 in this packet, and specifically at exercise #6. What relationship did we discover in that exercise?
We can utilize this concept in a variety of Regents-caliber exercises.
1)Which line below is parallel to y = -3x – 4?
(1)y = 3x + 2(3) y = x + 5
(2)y = x – 4(4) y = -3x + 1
2)Which line below is parallel to 6y – 12x = 24?
(1)y = 12x – 3(3) y = -2x - 7
(2)y = 2x – 5(4) y = -12x – 8
3)What is the slope of a line that is parallel to the line 2y = 3x + 10?
(1)(2) (3) 3(4) 5
4)Which line below is not parallel to y = 5x – 5?
(1)3y = 15x + 18(3) 5y = 10x - 25
(2)-4y = -20x+ 28(4) y – 5x = 2
The next few exercises will utilize the concept from the lesson on Day 4 with the material covered so far today.
5)What is the equation of a line parallel to y = 3x – 8 that goes through the point (1, 6)?
6)What is the equation of a line parallel to 7y + 21 = 7x that goes through the point (-4, 4)?
7)What is the equation of a line parallel to the 2y = x + 4 that goes through the point (0, 3)?
8)Are these lines parallel? Explain your answer.
Y = x – 66y = 4x + 8
9)Are these lines parallel? Explain your answer.
4x + 2y = 12-7y = -14x + 35
HOMEWORK: Worksheet
DAY 6 – DO NOW: REVIEW
1)What is the distance between the points (3, 5) and (6, 4), rounded to the nearest tenth.
2)The midpoint of PQ has coordinates (2, 0), and the coordinates of Q are (7, -2). What are the coordinates of P?
3)Are the lines y = -3 and y = 5 parallel? Explain your answer.
LESSON – SLOPES OF PERPENDICULAR LINES
**Let’s look back at Day 1 in this packet, and specifically at exercise #7. What relationship did we discover in that exercise?
We can utilize this concept in a variety of Regents-caliber exercises.
1)Which line below is perpendicular to the line y = 3x + 7?
(1)y = x + 5(3) y = -3x - 1
(2)y = -x – 4(4) y = 2x + 7
2)Which line below is perpendicular to the line y = x – 5?
(1)2y = 4x + 6(3) 6y = -12x - 6
(2)4y = -2x + 8(4) y – 2x = 1
3)What is the slope of a line that is perpendicular to the line y =- x?
(1) (2) - (3)- (4)
4)What is the slope of a line perpendicular to the line 3y + 3x = -6?
(1)1(2) -1(3) (4) -
5)Which line below is perpendicular to the line x = 1?
(1)x = -1(2) y = 3(3) y = x(4) y = x + 1
The next few exercises will utilize the concept from the lesson on Day 4 with the material covered so far today.
6)What is the equation of a line perpendicular to the line y = 4x + 1 that goes through the point
(-8, -2)?
7)What is the equation of a line perpendicular to the line 2y = -3x – 8 that goes through the point (6, 6)?
8)Are these lines parallel, perpendicular, or neither? Explain your answer.
y = x + 93y + 15x = 24
9)Are these lines parallel, perpendicular, or neither? Explain your answer.
4y = -7x + 20-14y = 8x + 32
Homework day 6 - page 311, #3-17 odd and #21
DAY 5 HOMEWORK
1)Which line below is parallel to y =x – 1?
(1)y = x + 2(3) y = 2x - 1
(2)y = x + 3(4) y = -x + 5
2)Which line below is parallel to 5y + 10 = 20x?
(1) y = 4x - 7(3) y = 3x + 2
(2) y = 20x - 8(4) y = -4x - 1
3)What is the slope of a line that is parallel to the line -3y = x – 6??
(1)1(2)3(3) (4) -
4)Which line below is not parallel to y = -x + 1?
(1)2y = -2x + 4(3) y – x + 10
(2)y + x = 5(4) -6y = 6x + 18
5)What is the equation of a line parallel to y = 2x + 6 that goes through the point (3, 1)?
6)What is the equation of a line parallel to 4y + 12x = 4 that goes through the point (-3, 9)?
7)What is the equation of a line parallel to 4y = 3x + 8 that goes through the point (8, 2)?
8)Are these lines parallel? Explain your answer.
y = x – 43y = 6x + 15
9)Are these lines parallel? Explain your answer.
Y – x = 8-3y = -3x - 3