<PRE><B>Question 1020439</B>
Given D is the midpoint of B and C, then points on AD are equidistant from points B and C.  AD is the perpendicular bisector.
:
Given gradient of BC is 3/4, the slope of line BC is 3/4, then
:
y = 3x/4 + b
:
: use point B, (0,-4) to find b
:
-4 = 3(0)/4 + b
:
b = -4
:
The equation of line BC is
:
y = 3x/4 -4
:
since AD is perpendicular to BC, the slope of AD is -4x/3
:
use point A, (5,6) to find b
:
6 = -4(5)/3 + b
:
18 = -20 + 3b
:
3b = 38
:
b = 38/3
:
**************************
Equation of AD is
:
y = -4x/3 + 38/3
**************************
:
Now set the two lines = to each other to find point D
:
3x/4 -4 = -4x/3 + 38/3
:
9x -48 = -16x + 152
:
25x = 200
:
x = 8
:
substitute for x in equation for BC
:
y = 3(8)/4 -4
:
y = 2
:
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point D is (8,2)
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