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Coordinate Geometry and Trigonometry Question?

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A (11, 5), B (5,11), C and D are the vertices of a parallelogram. The points P(17, 8) and Q(21,16) lie on AD and CD respectively. 

i)find the equation of AD and of CD 
ii)find the ratio DQ:QC 
iii)Show that triangle PDQ is isosceles
and also
A right angle triangle shows that AB=hm (adj) and BC= 6m (opp). The point D lies on BC so that BD = 1m and DC=5m. THe angle of CAD is 45 degrees and the angle BAD is an unknown degree (thater). By using the expansion of tan (thater + 45 degrees) or otherwise, find the possible values of h.

asked Apr 15, 2016 in GEOMETRY by anonymous

3 Answers

0 votes

(i)

Find the equation of and of .

Step 1:

Parallelogram has coordinate points and .

The points and lie on and .

Consider the coordinate points .

Formula for .

Substitute and in the slope formula.

General form of line equation is .

Substitute and image in the general form.

image

The line passing through the is image.

Step 2:

is lies on point of .

Substitute and in the slope formula.

Substitute and imagein the general form.

The line passing through the is image.

Step 3:

is lies on point of .

Here parallel to .

Slope of is .

Substitute image and image in the general form.

image

The line passing through the is image.

Solution :

line equation is image.

line equation is image.

answered Apr 15, 2016 by Anney Mentor
0 votes

(ii)

Find the ratio image.

Step 1:

The points and lie on and .

Find image.

Here and intersect lines.

The equations are image and image.

Solve the equations to find point image.

image

Divide each side by image.

image

Substitute image in image.

image

The point image is image.

Step 2:

From (i), image parallel to .

Slope of image is .

Substitute image and imagein the general form.

image

The line passing through the image is image.

Find image.

Here and image intersect lines.

Solve both equations to find point image.

image

Divide each side by image.

image

Substitute image in image.

image

The point image is image.

Substitute image and in the ratio of image.

image

Solution :

The ratio of image is image.

answered Apr 15, 2016 by Anney Mentor
0 votes

(iii)

Find is isosceles or not.

Step 1:

The Parallelogram has coordinate points and .

The points are and .

If the is an isosceles triangle, then .

Substitute and in the formula.

Substitute and in the formula.

Since, then is isosceles.

Solution :

then is isosceles.

answered Apr 15, 2016 by Anney Mentor

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