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32 The points A, B and C have coordinates (2, -5), (5, 9) and (-9, 12) respectively. (a) Find the vectors AB, BC and AC in column vector form. (b) Find AB, BC and AC. АВ (c) Show that AABC is an isosceles triangle. (d) Find the coordinates of a point D such that ABCD forms a rhombus. (e) Find the coordinates of the point of intersection of the diagonals of the rhombus ABCD.

32 The points A, B and C have coordinates (2, -5), (5, 9) and (-9, 12) respectively. (a) Find the vectors AB, BC and AC in column vector form. (b) Find AB, BC and AC. АВ (c) Show that AABC is an isosceles triangle. (d) Find the coordinates of a point D such that ABCD forms a rhombus. (e) Find the coordinates of the point of intersection of the diagonals of the rhombus ABCD.

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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32 The points A, B and C have coordinates (2, –5), (5, 9) and (-9, 12) respectively. (a) Find the vectors AB, BC and AC in column vector form. (b) Find|AB,|BC| and|AC. (c) Show that AABC is an isosceles triangle. (d) Find the coordinates of a point D such that ABCD forms a rhombus. (e) Find the coordinates of the point of intersection of the diagonals of the rhombus ABCD.
Transcribed Image Text:32 The points A, B and C have coordinates (2, –5), (5, 9) and (-9, 12) respectively. (a) Find the vectors AB, BC and AC in column vector form. (b) Find|AB,|BC| and|AC. (c) Show that AABC is an isosceles triangle. (d) Find the coordinates of a point D such that ABCD forms a rhombus. (e) Find the coordinates of the point of intersection of the diagonals of the rhombus ABCD.
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