math t

數學神童

two parallel lines passes through (5,0) and (-5,0) respectively,theyintersect with a straight line equation 4x+3y=25 at P and Q.If PQ is 5units, find the possible gradients of the parallel lines.

antimatter

Draw all the lines, with the two parallel lines go towards the upper right*. Shift down the line of 4x+3y=25 to 4x+3y=20. Then you will see a triangle with a base of length 10, and an arm on the right hand side with length 5. The angle between these two arms can be find through the gradient of the equation 4x+3y=20. Solve the triangle for the angle between the arm of length 10 and the third arm, and then convert it back to the gradient. Repeat the process and draw the lines (* above) to the lower right, then you will get another gradient.

This is a not-so-good but easier-to-explain method. I think this method can't let you express your solution in square root of something. There is another method, which you can calculate your gradient more exactly without using sine, cosine rules.

Jia you ^^