Question

1.) A highway runs east-west between two towns C and B that are 25km apart. Town A lies 15 km directly north from C. A straight road is built from A to meet the highway at D which is equidistant from A and B. Find the position of D on the highway.
2.) A,B, C and D are four points on the same staright line. The distances between successive points are equal. If A is (1,-3), C is (4,a) and D is (b,5), find the values of a and b.

Answer 1

Draw a diagram and if AD is x km, then use right triangle ACD to show that
(25-x)^2 + 15^2 = x^2
solve for x

In the ABCD line, using similar triangles,
a-3 = 2(5-a)
4-1 = 2(b-4)