A rectangle ABCD is to be drawn on a centimeter grid such that
A has coordinates (-4,-2)
B has coordinates (1,10)
C has coordinates (19,a)
D has coordinates (b,c)
(a) work out the value of a, the value of b and the value of c.
(b) calculate the perimeter, in centimeters , of rectangle ABCD
Answers
Given : A rectangle ABCD is to be drawn on a centimeter grid such that
A has coordinates (-4,-2)
B has coordinates (1,10)
C has coordinates (19,a)
D has coordinates (b,c)
To Find : (a) work out the value of a, the value of b and the value of c.
(b) calculate the perimeter, in centimeters , of rectangle ABCD
Solution :
A has coordinates (-4,-2)
B has coordinates (1,10)
C has coordinates (19,a)
D has coordinates (b,c)
AB = √(1 - (-4))² + (10 - (-2))² = √5² + 12² = 13
Slope of AB = (10 - (-2))/(1 - (-4)) = 12/5
Slope of BC and AD = - 5/12
Slope of CD = 12/5
Slope of BC = (a - 10)/(19 - 1) = - 5/12
=> a - 10 = -90/12
=> 12a - 120 = -90
=> 12a = 30
=> a = 2.5
BC = √(19 - 1)² + (2.5 - 10)² = 19.5
Perimeter = 2( 13 + 19.5) = 65 cm
Slope of AD = (c + 2)/(b + 4) = - 5/12
=> 12c + 24 = -5b - 20
=> 5b + 12c = -44
Slope of CD = (c - 5/2)/(b - 19) = 12/5
=> 5c - 25/2 = 12b - 228
=> 5c - 12b = -215.5
5b + 12c = -44
5c - 12b = -202.5
on solving
b = 14 , c = -9.5
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