and
are points on the parabola
such that
and
intersect on the
-axis. Determine the
-coordinate of
in terms of the
-coordinates of
and
, which are
and
respectively.
Solution:
Start out by graphing, and labeling lines
and
, such that all points
are on the line
. We label the point
, the point
, the point
, and the point
. The lines intersect at the y-axis, which we label to be point
. We start by finding the equation
is on. We put the line into the slope-intercept form
, where
is the slope and
is the y-intercept* . Since the line intersects the
at the point
, we know the y-intercept is
. The slope of the line is
. Therefore we have
. Substituting the point
into the equation gives us
. We could also substitute
into the equation to give us
as well. We now find the equation
is on. Again, put the line into slope-intercept form
, where
is slope, and
is y-intercept*. The lines
and
intersect at the point
, therefore the y-intercept of
is
. The slope of
is
. Therefore our new equation is
. Substituting either points
or
give
or
, where both can be simplified two after expanding and subtract
in the first equation, and
in the second equation to give
. We are now left with the two equations
and
. Subtracting the two equations results in
![]()
![]()
*(note: I changed the slope-intercept form from
to
to avoid any confusion with point
)
2007 ToT Spring Seniors A1: Coordinate Bashing
Reply