Question

1. if la = mk, lk = 7x - 10, mn = x + 3, mn = 9x - 1 and kj = 28. find la
2. if t is the mid - point of su, find x
3. if g is the mid - point of fh find fg
4. if r is the mid - point of qs, find qs
5. if b is the mid - point of ac, and ac = 8x - 20, find bc
6. if ef bisects cd, cg = 5x - 1, gd = 7x - 13, ef = 6x - 4, and gf = 13, find eg
7. if r is the mid - point of qs, rs = 2x - 4, st = 4x - 1, and rt = 8x - 43, find qs

Explanation:

Step1: Use mid - point property

If \(T\) is the mid - point of \(SU\), then \(ST = TU\). So, \(8x + 11=12x - 1\).

Step2: Solve for \(x\)

\(11 + 1=12x-8x\), \(4x = 12\), \(x = 3\).

Answer:

\(x = 3\)