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Revision worksheet: Analytical geometry C-3) A(4; 5), B(a;b) and C(8;-3) are the vertices of AABC. P(2; -1) is the midpoint of BC. 1. Calculate the values of a nd b, the coordinates of B. 2. Prove that AB LAC. 3.Determine the equation of AP.

Revision worksheet: Analytical geometry C-3) A(4; 5), B(a;b) and C(8;-3) are the vertices of AABC. P(2; -1) is the midpoint of BC. 1. Calculate the values of a nd b, the coordinates of B. 2. Prove that AB LAC. 3.Determine the equation of AP.

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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Revision worksheet: Analytical geometry Al4; 5) C-3) A(4; 5), B(a;b) and C(8; -3) are the vertices of AABC. P(2; -1) is the midpoint of BC. 1. Calculate the valnes of a and b, the coordinates of B. 2. Prove that AB LAC. 3.Determine the equation of AP. 4. IfB is the point (-4; 1), prove analyticąlly that AB = AC. 5 Determine the area of AABC. 6. Calculate the magnitude of cach of the following correct to one decimal place. All geometric reasons mmst be given. a) T, the inclination of AC b) S, the inclination of BC Af1; 7), B(3; t), C(5; –9) and D(-3; 3) are the vertices of trapezium ABCD, with AB | DC. P is the midpoint of DC. 2 Calculate the valae of r if AB || DC. 8. Determine the coordinates of P, the midpoint of DC. 9. Determine the equation of the straight line DC. 10. Determine the coordinafes of S, the x-intercept ofDC. 11. Find the length of AD, giving your answer in simplest surd form. 12. Calculate the magnitade of cach of the following correct to ane decimal place. All working must be shown. ) , the inclination angle of SA, if S is the point (-1; 0) b) A
Transcribed Image Text:Revision worksheet: Analytical geometry Al4; 5) C-3) A(4; 5), B(a;b) and C(8; -3) are the vertices of AABC. P(2; -1) is the midpoint of BC. 1. Calculate the valnes of a and b, the coordinates of B. 2. Prove that AB LAC. 3.Determine the equation of AP. 4. IfB is the point (-4; 1), prove analyticąlly that AB = AC. 5 Determine the area of AABC. 6. Calculate the magnitude of cach of the following correct to one decimal place. All geometric reasons mmst be given. a) T, the inclination of AC b) S, the inclination of BC Af1; 7), B(3; t), C(5; –9) and D(-3; 3) are the vertices of trapezium ABCD, with AB | DC. P is the midpoint of DC. 2 Calculate the valae of r if AB || DC. 8. Determine the coordinates of P, the midpoint of DC. 9. Determine the equation of the straight line DC. 10. Determine the coordinafes of S, the x-intercept ofDC. 11. Find the length of AD, giving your answer in simplest surd form. 12. Calculate the magnitade of cach of the following correct to ane decimal place. All working must be shown. ) , the inclination angle of SA, if S is the point (-1; 0) b) A
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Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

 

Given:

A:4,5, B:a,b and C:8,-3 are the vertices of ∆ABC.

P:2,-1 is the midpoint of BC.

 

1. To calculate the values of a and b; the coordinates of B.

2. To prove that AB⊥AC.

3. To determine the equation of AP.

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