# Thread: Solving problem involving equations of straight lines

1. ## Solving problem involving equations of straight lines

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

Find
(a) the equation of $\displaystyle AB$

(b)the coordinates of point $\displaystyle C$

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

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

Find
(a) the equation of $\displaystyle AB$

(b)the coordinates of point $\displaystyle C$

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

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

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

Find
(a) the equation of $\displaystyle AB$

(b)the coordinates of point $\displaystyle C$

(c)the equation of locus of a moving point such that its distance from point $\displaystyle A$ is twice distance from $\displaystyle D$
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 $\displaystyle m_1 \cdot m_2 = -1$ )

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)

4. 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.

5. can anybody show the step how to get the answer??

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

Tonio

,

,

,

,

,

,

,

,

,

,

,

,

,

# problem involving line

Click on a term to search for related topics.