Question

Please please please help. I'm in honor's geometry and if I don't get my grade at least to a C, I'm going to fail

In the diagram below, m is the perpendicular bisector of BC.
If BK = 5x, AC = 6x + 7, CP = 4x, AB = 9x – 14. Find BC

Answer 1

BC = 56 units

Explanation:

since the main diagonal AK bisects the diagonal BC , then the figure is a kite.

• the disjoint pairs of consecutive sides are congruent in a kite, that is

AB = AC and BK = CK

using the pair AB = AC to solve for x

9x - 14 = 6x + 7 ( subtract 6x from both sides )

3x - 14 = 7 ( add 14 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Since m bisects BC , then

CP = PB and

BC = CP + PB = 4x + 4x = 8x

then

BC = 8x = 8 × 7 = 56