Part a:1 .P and Q are the points of intersection of the line y/2 + x/3= 1 with the x and y axes repectively. The gradient of QR is 1/2, where R is the point with x-coordinate 2a,a>0.
a. Find the y-coordinate of R in terms of a
b.Find the value of a if the gradient of PR is -2
P(3,0), Q(0,2), R(2a,?)
If we find the rule for the line connecting points Q and R, we can then substitute 2a into that equation to find y in terms of a.
y intercept is 2 and gradient is 1/2, equation between Q and R is
so y coordinate or R in terms of a is
Equation of line R and P has gradient of -2 and x intercept at (3,0)
Finding the equation between the 2 points..
notice R is the intersection between the 2 lines with equations:
Simply let y=y in those 2 equations to find x coordinate of the intersection which is 2a.
multiply everything by 2 (so x is no longer a fraction)
get x by itself
we were told to find a: now