Question

* Three points of a quadrilateral ABCD are A(1, 2), B(6, 7) and C19,6). Given that AB = AD and BC = DC and F is the foot of the perpendicular from B to the line AC. Find the coordinates of D​

Answer 1

Answer:

recognize that AB=AD means DAB makes an isosceles triangle with angles B and D as base angles and angle A as vertex angle

2 exact same thing for BC = DC. DCB makes an isosceles triangle with angles B and D as base angles and angle c as vertex angle

3 a line from angle A to the midpoint of BC is a perpendicular bisector of BD

4 exact same thing for DCB applies. a line from angle C to the midpoint of BD is a perpendicular bisector of line BD

5 steps 4 and 5 should tell you that the lines BD and AC are perpendicular bisectors of each other

STEPS

1 find the slop of AC

2 find the slop of BD using the slop of AC slop(BD)=1/slop(AC)

3 find the midpoint of AC, which is also the midpoint of BD. call that midpoint 'O"

4 find the distance from B to or (OB) which is equal to OD (the distance from "o" to D using distance formula

5 use the distance OD to find the coordinates of D