Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them lie on a l...
Let A, B, C, and D be four distinct points in the plane. Suppose
that no three of them lie on a line and A, C are on opposite sides
of the line BD. The lengths of the line segments AB, BC, CD and DA
are 1, 2, 3 and 4 respectively.
(a) What is the range of possible values for the length x of the
line segment BD? You should justify your answer carefully! [5
marks]
(b) Now suppose that x = 4. What is the length of the line segment
AC? [13 marks]
Homework Answers
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Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them lie on a l...
Trigonometry
Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them lie on a line and A, C are on opposite sides of the line BD. The lengths of the line segments AB, BC, CD and DA are 1, 2, 3 and 4 respectively. (a) What is the range of possible values for the length x of the line segment BD?
hint for d): consider a point D such that M is the midpoint of CD. Which...
hint for d): consider a point D such that M is the
midpoint of CD. Which segments are congruent here? Do you see a
triangle with all three side lengts given.
Could you please write some instructions on the side
so I know how to follow your solution?
5. Given a triangle ABC, let M be the midpoint of the segment AB. The segment CM is called the median of the triangle. Let T be the point on the line...
Let A-B-C denote B is between A and C. For this problem, use the following three...
Let A-B-C denote B is between A and C. For this problem, use the following three axioms: A1: Each pair of points is assigned a number, called the distance between A and B. it is denoted by AB. A2: Given any points A and B, then AB 20. Equality holds precisely when A=B. A3: For all points A and B, ABEBA Suppose A, B, C, and D are collinear. Assume that A-B-C means: A, B, and C are distinct, collinear...
(1) Assume the axioms of metric geometry. Let A, B, C, D be distinct collinear points....
(1) Assume the axioms of metric geometry. Let A, B, C, D be
distinct collinear points. Let f : l → R be a coordinate function
for the line l that crosses all of A, B, C, D. Suppose f(A) <
f(B) < f(C) < f(D). Prove that AD = AB ∪ BC ∪ CD. (2) Assume
the axioms of metric geometry. Let A, B, C, D be distinct collinear
points. Suppose A ∗ B ∗ C and B ∗...
Let A, B, C be three collinear points and let D, E, F be the midpoints...
Let A, B, C be three collinear points and let D, E, F be the midpoints of segments AB, BC, and AC, respectively. Prove that the segments DE and BF have the same midpoint. Let d be a line and let A, B, C be three points not on d. Prove that if d does not separate points A and B and it does not separate points B and C, then it does not separate points A and C.
VA $ d B ABCD is not a rhombus because the slope of the diagonals are...
VA $ d B ABCD is not a rhombus because the slope of the diagonals are opposite reciprocals. ABCD is not a rhombus. The lengths of AD and BC is 4.1 units but the lengths of AB and DC is 6 units. ABCD is a rhombus because sides AB and DC have a slope of 2 and sides BC and AD have a slope of zero. The opposite sides of a rhombus must have the same slope to be parallel....
You are given the four points in the plane a=(-2,2), b=(1,-3), c=(3,6), and d=(7,-3)
You are given the four points in the plane a=(-2,2), b=(1,-3), c=(3,6), and d=(7,-3). The graph of the function consists of the three line segments AB, BC and CD. Find the integral by interpreting the integral in terms of sums and/or differences of areas of elementary figures
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and D The graph of the function f(z) consists of the three line segments AB, BC and CD...
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and D The graph of the function f(z) consists of the three line segments AB, BC and CD (11, -2) Find the integralf() dz by interpreting the integral in terms of sums and/or differences of areas of elementary figures f(z) de-
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and...
I need help doing a doing two column for these two propositions. Book 1 Proposition 7:...
I need help doing a doing two column for these two
propositions.
Book 1 Proposition 7:
Given two straight lines constructed from the ends of a straight
line and meeting in a point, there cannot be constructed from the
ends of the same straight line, and on the same side of it, two
other straight lines meeting in another point and equal to the
former two respectively, namely each equal to that from the same
end.
Book 3 Proposition 14:...
(1 point) You are given the four points in the plane A = (0,7), B=(2, -7),...
(1 point) You are given the four points in the plane A = (0,7), B=(2, -7), C = (5,1), and D= (10,-2). The graph of the function f(x) consists of the 10 three line segments AB, BC and CD. Find the integral f(x) dx by interpreting the integral in terms of sums and/or differences of areas of elementary Jo figures. 10 f(x) dx =
hint for d): consider a point D such that M is the
midpoint of CD. Which segments are congruent here? Do you see a
triangle with all three side lengts given.
Could you please write some instructions on the side
so I know how to follow your solution?
5. Given a triangle ABC, let M be the midpoint of the segment AB. The segment CM is called the median of the triangle. Let T be the point on the line...
Let A-B-C denote B is between A and C. For this problem, use the following three axioms: A1: Each pair of points is assigned a number, called the distance between A and B. it is denoted by AB. A2: Given any points A and B, then AB 20. Equality holds precisely when A=B. A3: For all points A and B, ABEBA Suppose A, B, C, and D are collinear. Assume that A-B-C means: A, B, and C are distinct, collinear...
(1) Assume the axioms of metric geometry. Let A, B, C, D be
distinct collinear points. Let f : l → R be a coordinate function
for the line l that crosses all of A, B, C, D. Suppose f(A) <
f(B) < f(C) < f(D). Prove that AD = AB ∪ BC ∪ CD. (2) Assume
the axioms of metric geometry. Let A, B, C, D be distinct collinear
points. Suppose A ∗ B ∗ C and B ∗...
Let A, B, C be three collinear points and let D, E, F be the midpoints of segments AB, BC, and AC, respectively. Prove that the segments DE and BF have the same midpoint. Let d be a line and let A, B, C be three points not on d. Prove that if d does not separate points A and B and it does not separate points B and C, then it does not separate points A and C.
VA $ d B ABCD is not a rhombus because the slope of the diagonals are opposite reciprocals. ABCD is not a rhombus. The lengths of AD and BC is 4.1 units but the lengths of AB and DC is 6 units. ABCD is a rhombus because sides AB and DC have a slope of 2 and sides BC and AD have a slope of zero. The opposite sides of a rhombus must have the same slope to be parallel....
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and D The graph of the function f(z) consists of the three line segments AB, BC and CD (11, -2) Find the integralf() dz by interpreting the integral in terms of sums and/or differences of areas of elementary figures f(z) de-
Previous ProblemPlUDIelfLis (1 point) You are given the four points in the plane A (1,1), B- (4,-2), C (7,2), and...
I need help doing a doing two column for these two
propositions.
Book 1 Proposition 7:
Given two straight lines constructed from the ends of a straight
line and meeting in a point, there cannot be constructed from the
ends of the same straight line, and on the same side of it, two
other straight lines meeting in another point and equal to the
former two respectively, namely each equal to that from the same
end.
Book 3 Proposition 14:...
(1 point) You are given the four points in the plane A = (0,7), B=(2, -7), C = (5,1), and D= (10,-2). The graph of the function f(x) consists of the 10 three line segments AB, BC and CD. Find the integral f(x) dx by interpreting the integral in terms of sums and/or differences of areas of elementary Jo figures. 10 f(x) dx =
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