# Homework Help: Distintion Maths Challenge

1. Mar 13, 2005

### aek

Distinction Maths Challenge

the line 2x + 3y-8=0 cuts the x and y axis at A and B respectively. The line y=ax+7 is called l. Find

a). in terms of a, the coordinates of the point where l cuts AB (extended).

b). the value of a if l is to divide AB internally in the ratio of 1:3.

Last edited: Mar 13, 2005
2. Mar 13, 2005

### Andrew Mason

If I cuts AB then the point of intersection (x,y) is a solution to the equations of both lines. So just equate the two and get the expression for x and y in terms of a.

$$2x + 3(ax + 7) - 8 = 0$$ so:

$$x = -13/(3a + 2)$$

Do the same thing for y.

A and B are the respective intersections of lines x=0 and y=0 with the line 2x + 3y-8=0. The points (0,A) (B,0) and (0,0) form a triangle with lengths A0B. Find A and B.

If I divides AB at P in a ratio of 1:3 (ie PB/AP = 3) what is the ratio of the x coordinate at P to the x coordinate at B? (draw a vertical line from P to the x axis (intersecting at x') and compare triangles A0B to Px'B). That will give you the x coordinate of P.

Just substitute the x coordinate of P into the expression for a from 1. to find a.

AM