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Show that Congruence Axiom 1 fails. (Hint. Consider the line segment from A = (0, 0) to B = (1, 1). ‹en consider the points P = (1, 0) and Q = (2, 0). Use the distance formula D((x1, y1), (x2, y2)) = √(x1 − x2)2 + (y1 − y2)2 to show that there is no point R on −−→ P Q so that AB ∼= P R.)

Show that Congruence Axiom 1 fails. (Hint. Consider the line segment from A = (0, 0) to B = (1, 1). ‹en consider the points P = (1, 0) and Q = (2, 0). Use the distance formula D((x1, y1), (x2, y2)) = √(x1 − x2)2 + (y1 − y2)2 to show that there is no point R on −−→ P Q so that AB ∼= P R.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show that Congruence Axiom 1 fails. (Hint. Consider the line segment from A = (0, 0) to B = (1, 1). ‹en
consider the points P = (1, 0) and Q = (2, 0). Use the distance formula
D((x1, y1), (x2, y2)) = √(x1 − x2)2 + (y1 − y2)2
to show that there is no point R on −−→
P Q so that AB ∼= P R.)

Show that axiom C1 fails. (Hint. Consider the line segment from A = (0,0) to B = (1, 1). Then consider the points P = (1,0) and Q = (2,0). Use the distance formula D((*1, 1), (2, 2)) = √√(x1 − 2)² + (31 — Y2)² to show that there is no point R on PQ so that AB ≈ PR.)
Transcribed Image Text:Show that axiom C1 fails. (Hint. Consider the line segment from A = (0,0) to B = (1, 1). Then consider the points P = (1,0) and Q = (2,0). Use the distance formula D((*1, 1), (2, 2)) = √√(x1 − 2)² + (31 — Y2)² to show that there is no point R on PQ so that AB ≈ PR.)
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