# Solving problem involving equations of straight lines

• Mar 26th 2010, 11:29 PM
mastermin346
Solving problem involving equations of straight lines
Diagram 4 shows an equilateral $ABCD$.Given that $C$ lies on the perpendicular bisector of $AD$ and the equation of $DC$ is $x=5y-17$

Find
(a) the equation of $AB$

(b)the coordinates of point $C$

(c)the equation of locus of a moving point such that its distance from point $A$ is twice distance from $D$
• Mar 27th 2010, 02:46 AM
tonio
Quote:

Originally Posted by mastermin346
Diagram 4 shows an equilateral $ABCD$.Given that $C$ lies on the perpendicular bisector of $AD$ and the equation of $DC$ is $x=5y-17$

Find
(a) the equation of $AB$

(b)the coordinates of point $C$

(c)the equation of locus of a moving point such that its distance from point $A$ is twice distance from $D$

what've you done so far? What is the perpendicular bisector of a line segment? How do you find the middle point of a segment? Where are you stuck?
All this is standard stuff in analytic geometry, you must have studied it: show us your effort to solve the question.

Tonio
• Mar 27th 2010, 02:49 AM
earboth
Quote:

Originally Posted by mastermin346
Diagram 4 shows an equilateral $ABCD$.Given that $C$ lies on the perpendicular bisector of $AD$ and the equation of $DC$ is $x=5y-17$

Find
(a) the equation of $AB$

(b)the coordinates of point $C$

(c)the equation of locus of a moving point such that its distance from point $A$ is twice distance from $D$

1. Calculate the coordinates of the midpoint of AD.

2. Calculate the slope of AD and consequently the slope perpendicular to AD.
(Hint: 2 lines are perpendicular if their slopes satisfy $m_1 \cdot m_2 = -1$ )

3. AB has the same slope as the perpendicular bisector and must pass through A.

4. The point C is the point of intersection of the perpendicular bisector and the given line. I've got C(8, 5)
• Mar 27th 2010, 02:50 AM
sa-ri-ga-ma
i) Find the mid point of AD. Let it be P.
ii) Find the slope m of AD
iii) Slope of CP = -1/m, because AD is perpendicular to CP
iv) Find the equation of CP.
v) Find the point of intersection of CP and CD. That gives you the co-ordinates of C.
vi) Sole of AB is the same as the slope of PC.
vii) Point A is given. Find the equation of AB.
• Mar 27th 2010, 05:42 AM
mastermin346
can anybody show the step how to get the answer??
• Mar 27th 2010, 09:23 AM
tonio
Quote:

Originally Posted by mastermin346
can anybody show the step how to get the answer??