How to answer this questions: coordinates of the midpoints and finding the equations of lines AC?

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1 Answer
Jim G.
Jan 30, 2018

#"see explanation"#

Explanation:

#(a)#

#"given "A(x_1,y_1)" and "B(x_2,y_2)#

#"then the coordinates of the midpoint (M) of AB"#

#•color(white)(x)M=[1/2(x_1+x_2),1/2(y_1+y_2)]#

#rArrM=[1/2(9+5),1/2(10+0)]=(7,5)#

#rArrN=[1/2(9+13),1/2(10+0)]=(11,5)#

#(b)#

#"equations of lines AC and BC"#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"calculate the slope m using the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#rArrm_(AC)=(10-0)/(9-5)=10/4=5/2#

#rArry=5/2x+blarrcolor(blue)"partial equation"#

#"to find b substitute the coordinates of either A or C"#
#"into the partial equation"#

#"using "A(5,0)" then"#

#0=25/2+brArrb=-25/2#

#rArry=5/2x-25/2larrcolor(blue)"equation of AC"#

#"Similarly for the equation of BC"#

#m_(BC)=(10-0)/(9-13)=10/(-4)=-5/2#

#rArry=-5/2x+b#

#"using "B(13,0)" then"#

#0=-65/2+brArrb=65/2#

#rArry=-5/2x+65/2larrcolor(blue)"equation of BC"#

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