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let E be the point where this perpendicular line through c intersects AB. Calculate the cordinates of E .( C =(4,-2) , A=(3,6) B=(-6,0).

Also which is shorter distance. [CD] or [CE]? Find this distance.

I have no clue what to do .

1. qed2923

Find slope & eqt of AB.

find eqt of perpendicular line through c. Use perpendicular slope slope to AB

E = pt of intersection of the two lines.

No pt D ???

2. Ms. L. Witter

You found D in an earlier part of the question - I think it was the midpoint part of the question.

3. Aedamar

Hi Vicky if you post the exact question, even a picture of it i can help you.

4. helena12140

you use fomula?

5. Leetkd

this is in the exam papers yes what year and question

6. Dazzla16

Hey Vicky!

This is what you do:

Find the slope of AB

The slope of AB is:

y2 - y1

_____ =

x2 - x1

(0) - (6)

______ =

(-6) - 3

-6/-9= 2/3

That means the perpendicular slope is -3/2

Now you have to find the equation of the line with point C (4, -2) and a slope of -3/2

This is how:

y - y1 = m(x - x1)

y - (-2) = -3/2(x - (4))

y + 2 = -3/2x + 6

y = -3/2x + 4

That is the equation of the line with point C and a slope of -3/2

Now you have to find the intersection point of the lines [AB] and C to locate E.

First, we need to find the equation of the line [AB]

y - y1 = m(x - x1)

y - (6) = 2/3(x - (3))

y - 6 = 2/3x - 2

y = 2/3x + 4

Then use your two equations to solve simultaneous equations to find the point E

Rearrange the two equations so that the variables (numbers with letters) are on one side, and a number on the other side

3/2x + y = 4

-2/3x + y = 4

You can now solve these simultaneous equations. Just subtract the equations.

You end up getting:

13/6x = 0

x = 0

Substitute it back in to one of the equations:

3/2(0) + y = 4

y = 4

The point E is located at (0,4)

There you go!

By the way, you never gave information about point D. But anyway, here's the distance of [CE]

[CE] = square root((x2 - x1)^2 + (y2 - y1)^2)

= square root((4 - 0)^2 + (-2 - 4)^2)

= square root(4^2 + (-6)^2)

= square root(16 + 36)

= square root(52)

= 2(square root(13))