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