Respuesta :
The point (2,0) on the x-axis lies on the line that passes through point C and is parallel to line AB.
Given:
A line AB goes through (-4, 0) and (2, -3).
Point C is at (-2, 2).
To find:
A point on the x-axis lies on the line that passes through point C and is parallel to line AB.
Solution:
A line passing through (-4,0) and (2,-3), the slope of the line be will be given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-0}{2-(-4)}=\frac{-3}{6}=\frac{-1}{2}[/tex]
Another line passing through point C (-2,2) parallel to line AB.
When the two lines are parallel their slopes are equal.
The slope of a line passing through point C =[tex]m =\frac{-1}{2}[/tex]
The equation of the line through point C (-2,2) will be
[tex](y-y_1)=m(x-x_1)\\\\(y-2)=\frac{-1}{2}(x-(-2))\\\\2(y-2)=-x-2\\\\2y-4=-x-2\\\\x+2y=4-2\\\\x+2y=2[/tex]
The point on the x-axis lies on the line that passes through point C will be determined by keeping y equal to 0 in its line equation.
[tex]x+2y=2\\\\Put, y=0\\\\x+2\times 0=2\\\\x=2[/tex]
The point (2,0) on the x-axis lies on the line that passes through point C and is parallel to line AB.
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