Quadrilateral ABCD has vertices A(-1, 5), B(4, 4), C(5, -3) and D(-4, -2). Quadrilateral SQUR is drawn with its vertices at the midpoints of the sides of quadrilateral ABCD. a) What are the coordinates of the vertices of the quadrilateral SQUR? b) Show that quadrilateral SQUR is a square by showing: i. that all its sides are the same length that there is a right angle at each corner (i.e. the two adjacent lines are perpendicular) ii. c) Find the equation of the line through A and C.

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Quadrilateral ABCD has vertices A(-1, 5), B(4, 4), C(5, -3) and D(-4, -2). Quadrilateral
SQUR is drawn with its vertices at the midpoints of the sides of quadrilateral ABCD.
a) What are the coordinates of the vertices of the quadrilateral SQUR?
b) Show that quadrilateral SQUR is a square by showing:
i.
that all its sides are the same length
ii. that there is a right angle at each corner (i.e. the two adjacent lines are
perpendicular)
c) Find the equation of the line through A and C.
d)
Find the equation of the line through B that is perpendicular to the line in
(c).
i.
ii.
Is the vertex D on this line in part d) (i)?
Transcribed Image Text:Quadrilateral ABCD has vertices A(-1, 5), B(4, 4), C(5, -3) and D(-4, -2). Quadrilateral SQUR is drawn with its vertices at the midpoints of the sides of quadrilateral ABCD. a) What are the coordinates of the vertices of the quadrilateral SQUR? b) Show that quadrilateral SQUR is a square by showing: i. that all its sides are the same length ii. that there is a right angle at each corner (i.e. the two adjacent lines are perpendicular) c) Find the equation of the line through A and C. d) Find the equation of the line through B that is perpendicular to the line in (c). i. ii. Is the vertex D on this line in part d) (i)?
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