Question

Please solve with explanation

Answer 1

Answer:

The x coordinate of S is b.

Step-by-step explanation:

a)

The coordinates of Point Q are:

(2a+2b)/2, 2c/2

= [(a + b), c].

The slope of the line AB

= (0-2c)/(2b-2a)

= -c/(b-a)

So The slope of the line QS = (b - a) / c = (b - a)/c.

Its equation is

y - c = (b - a)/c ( x - (a+b))

y = (b - a)/c ( x - (a+b)) + c.

The coordinates of Point P are:

(2a+0)/2, 2(c+ 0)/2

= (a, c)

The slope of the line AO

= (2c)/2a

= c/a

So The slope of the line PS = -a/c

Its equation is

y - c =  -a/c(x - a)

y  =  -a/c(x - a) + c

b)

So:

(b - a)/c ( x - (a+b)) + c

=  -a/c(x - a) + c

(b - a)(x - a - b) + c^2 = -a(x - a) + c^2

(b - a)(x - a - b) = -a(x - a)

bx - ab - b^2  - ax + a^2 + ab = -ax + a^2

bx - ax + ax + a^2 - a^2 - ab + ab = b^2

bx  =  b^2

x = b = the x coordinate of S.

c). The point R has the same x coordinate as S So RS is perpendicular to OB.