Question #43f13
1 Answer
Rectangle
Explanation:
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Find location of
#B# :
Given: The midpoint of#AB (1,5)# is up 3 and over 4 from#A# .#m_(AB) = 3/4# . This means#B# is up 3 and over 4 from (1,5):#B(5, 8), " and AB = 10# -
Find location of
#D# :
Given:#m_(DA) = -4/3 = -1/(m_(AB))# ,#" so " AB " perpendicular " DA = 90^@#
From A go down 4, over 3:#D (0, -2)#
Note: Since we don't know the length of#DA# , the location of D can vary. -
Find location of
#C# :
Given:#CD# and#DA# are#90^@# this means they are perpendicular.#m_(DA) = -4/3 = -1/(m_(CD)), m_(CD) = 3/4 = m_(AB)# . This means#CD |\| AB#
Given:#CD = 10# , using Pythagorean Theorem:#10^2 = (4x)^2 +(3x)^2#
#100 = 16x^2 + 9x^2#
#100 = 25x^2#
#x^2 = 4#
#x = 2# ,#" so " 4x = 8# ,#3x = 6#
This means from#D# we need to go up 8, over 6 from#D# to find#C (8, 4)#
Note: The location of#C# depends on#D# , which can vary. This means we don't know the length of#DA# or#AB# . -
Find the
#m_(BC ) = (y_2 - y_1)/(x_2 - x_1) = (8 - 4)/(5-8) = 4/-3 = -4/3# #" so " BC " is perpendicular to " AB#
So