Download Coordinate Geometry: Slope, Midpoints, and Segment Splitting and more Exams Nursing in PDF only on Docsity!
slope and midpoints lessons 1-5(Latest
Exam 2024)
lesson 1 - correct answers ✅slope and parallel lines examine the following lines and answer the question. given that line a is parallel to line b and the slope of line a is 2, what is the slope of line b? - correct answers ✅ 2 line l contains the points a(-2, 2) and b(-1, 0), and line k contains the points c(0, 4) and d(1, 2) are lines l and k, parallel? justify your response. - correct answers ✅yes, both lines have a slope of -2, so they are parallel. use the diagram to answer the question. if cyrus knows that abc ~ edc and ab || ed, how can he prove that like m passing through ab has the same slope as line l passing through ed? - correct answers ✅cyrus can use properties of similar triangles to show that ac/ec = bc/dc. then, by the multiplication property of equality, ac/bc = ec/dc. by the slope formula, the slope of line m = -ac/bc and the slope of line l = -ec/dc. thus, the slopes are equal. which equation in slope-intercept form represents a line that passes through the point (5, -1) and is parallel to the line y = 2x - 7? - correct answers ✅y = 2x - 11
slope and midpoints lessons 1-5(Latest
Exam 2024)
which equation in slope-intercept form represents a line that passes through the point (2, 3) and is parallel to the line y - 9 = 2/3(x + 7)? - correct answers ✅y = 2/3x + 5/ allana knows that xyz ~ uvz and xy || uv. what segment relationships can allana use to prove that the slope of line l is equal to the slope of line m? - correct answers ✅allana can show that uz/xz = vz/yz using the properties of similar triangles. then, uz/vz = xz/yz by the multiplicative property of equality. so, the slopes are equal by the slope formula. which equation in slope-intercept form represents a line that is parallel to y = 1/2x - 2 and passes through the point (-8, 1)? - correct answers ✅y = 1/2x + 5 which equation in slope-intercept form represents a line that is parallel to y = -4x - 5 and passes through the point (0, 0)? - correct answers ✅y = -4x line l contains the points a(2, 2) and b(3, 6). line k contains the points c(0, 5) and d(1, 9).
slope and midpoints lessons 1-5(Latest
Exam 2024)
match each of the four lines with a line that is perpendicular to it. - correct answers ✅y = 5/6x - 7 : y = -6/5x + 1 y = -5/6x - 8 : y = 6/5x - 5 y = -7/4x - 1 : y = 4/7x + 9 y = 7/4x - 2 : y = -4/7x + 2 use the diagram and given information to answer the question. using the given information, how can it be proved that lines l and m have slopes that are opposite reciprocals? - correct answers ✅since similar triangles have proportional sides, use the proportion bc/ab = de/cd. show that the slope of l = de/cd and the slope of m = -ab/bc. then show that bc/ab(-ab/bc) = -1, so the slopes of l and m are opposite reciprocals. which equation in slope-intercept form represents a line that passes through the point (6, -1) and is perpendicular to the line y = 2x - 7? - correct answers ✅y = -1/2x + 2
slope and midpoints lessons 1-5(Latest
Exam 2024)
which equation in slope-intercept form represents a line that passes through the point (2, 3) and is perpendicular to the line y - 9 = 2/3(x + 7)? - correct answers ✅y = - 3/2x + 6 use the diagram and given information to answer the question. what description shows that lines l and m have slopes that are opposite reciprocals? - correct answers ✅the triangles are similar, so ab/bc = cd/de. the slope of l = ab/bc and the slope of m = -de/cd. since cd/de and -de/cd are opposite reciprocals, lines l and m have slopes that are opposite reciprocals. what is the equation of the lines that passes through the given point and is perpendicular to the given line? point: (1, 1) line: y = 1/5x + 4/5 - correct answers ✅y = -5x + 6 use the equation and given point to answer the questions below.
slope and midpoints lessons 1-5(Latest
Exam 2024)
- match each numbered statement with the correct reason. - correct answers ✅1. given
- slope formula
- lines with equal slopes are parallel.
- both sets of opposite sides of a parallelogram are parallel.
- match each numbered statement with the correct reason. - correct answers ✅1. given
- slope formula
- multiply
- if the product of the slopes of two nonvertical lines is −1 the lines are perpendicular.
- perpendicular lines intersect to form right angles.
slope and midpoints lessons 1-5(Latest
Exam 2024)
- if a quadrilateral has four right angles, then it is a rectangle.
- match each numbered statement with the correct reason. - correct answers ✅1. given
- slope formula
- multiply
- if the product of the slopes of two nonvertical lines is −1 the lines are perpendicular.
- perpendicular lines intersect to form right angles.
- definition of right triangle
- match each numbered statement with the correct reason. - correct answers ✅1. given
- slope formula
slope and midpoints lessons 1-5(Latest
Exam 2024)
- multiply
- if the product of the slopes of two nonvertical lines is −1, the lines are perpendicular.
- perpendicular lines intersect to form right angles.
- if a quadrilateral has four right angles, then it is a rectangle. which reason justifies statement 3? - correct answers ✅lines with equal slopes are parallel. lesson 4 - correct answers ✅the midpoint formula ab has endpoints at a(2, 6) and b(6, 8) what are the coordinates of the midpoint? - correct answers ✅(4,7)
slope and midpoints lessons 1-5(Latest
Exam 2024)
the segment shown is half of ab, where b(−5, 1) is one endpoint of the segment and m(−3, 3) is the midpoint of the segment. what are the coordinates of point a? - correct answers ✅(-1, 5) cd has endpoints c and d, with c at coordinates (5, 8). cd has midpoint M at (3, 9). what are the coordinates of point d? - correct answers ✅(1, 10) which plan for a proof for this problem will show that quadrilateral abdc is a parallelogram? - correct answers ✅use the midpoint formula to find the midpoint of ad and bc. show that the midpoint for both segments is the same. by the definition of midpoint and bisect, ad and bc bisect each other. since the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. match each numbered statement with the correct reason.
- correct answers ✅1. given
slope and midpoints lessons 1-5(Latest
Exam 2024)
- midpoint formula
- if two points have the same coordinates, then they are the same point.
- definition of midsegment point b is at (3, 1). for which segment is b a midpoint? - correct answers ✅ac with endpoints at a(1, -1) and c(5, 3) which information about the coordinates of p will prove that fp is a median of △def? - correct answers ✅p(0.5, 5) which method will allow you to show ac and bd bisect each other? - correct answers ✅find the midpoints of ac and bd using the midpoint formula. if the midpoints have the same coordinates, then the segments intersect at their midpoints.
slope and midpoints lessons 1-5(Latest
Exam 2024)
which information about the coordinates of g and h will prove that gh is a median of △abc? - correct answers ✅g(3, -4) and h(8, 1) use the following information to complete the problem. given: quadrilateral abcd has vertices at a(3, 6), b(2, 2), c(−5, 4), and d(−4, 8). prove: quadrilateral abcd is a parallelogram. match each numbered statement with the correct reason.
- correct answers ✅1. given
- midpoint formula
- if two lines intersect, then their intersection is exactly one point.
- definition of midpoint
- definition of bisect
slope and midpoints lessons 1-5(Latest
Exam 2024)
line segment ab has endpoints a(1, 8) and b(7, −4). what are the coordinates of the point located 1/6 of the way from a to b? - correct answers ✅(2, 6) line segment ab has endpoints a(−5, −8) and b(2, 6). what are the coordinates of the point that partitions ab according to the part-to-part ratio 4:3? - correct answers ✅(-1, 0) line segment ba has endpoints b(−6, 1) and a(4, 6). what are the coordinates of the point that partitions ba according to the part-to-part ratio 2:3? - correct answers ✅(-2, 3) line segment ab has endpoints a(−1, 6) and b(5, −6). what are the coordinates of the point that partitions ab according to the part-to-part ratio 1:5? - correct answers ✅(0, 4)
