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

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1 Answer
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"