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#1
the line l(1 )passes through the points p(-2,4) and Q(8,9).

a) Find an equation for l(1) in the form of y=mx+c, where m an c are constants. The line l(2) passes through the point R(10,0) and is perpendicular to l(1). The line l(1) and l(2) intersect at the point S.

b) Calculate the coordinates of S.
c) Show the that the length of RS is (Squared root 80).
d) Hence, or otherwise, find the exact are of triangle PQR.
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4 years ago
#2
To start you off For a) m= y2-y1/x2-x1, and then think about the value of x for y=c in order to find c.
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4 years ago
#3
a) Use the equation (y-y1)/(y2-y1) = (x-x1)/(x2-x1) and plug in the values from the equation and rearrange.
b) If l(2) is perpendicular, it's gradient = -1 / gradient of l(1). Then you plug that m into the equation y-y1 = m(x-x1) with the value of point R. Rearrange and that will give you the equation of l(2), write it in y=mx+c. The point at which they intersect is when the part after y= are equal for both equations. So you just form an equation using that and solve it for x, then solve it for y by plugging x into one of the equations of the lines.
c) The length of RS can be found using pythagoras' thereom where distance^2 = changeInX^2 + changeInY^2. Plug in the values for how much x and y changes from R to S.
d) The triangle PQR can be split with the line RS to form two right angled triangles. (RS is the altitude from R). Work out the areas of the two right angled triangles and add them together. The area of a right angled triangle is = 1/2 * leg 1 * leg 2. The legs of a triangle are the non-hypotenuse sides.
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