Question

Please help me out! :)

Answer 1

answer is;

b

explanation

magnitude of two points is given by;

√{(x2-x1)^2+(y1-y2)^2}

for RS we have,

√{(b-0)^2+(c-a)^2}

=√{(b)^2+(c-a)^2}

Answer 2

To find the length of a segment you can use the pythagorean theorem: given two points $A=(x_A,y_B),\ B=(x_B,y_B)$ you have

$\overline{AB} = \sqrt{(x_A-x_B)^2+(y_A-y_B)^2}$

In your case, we have

$\overline{RS} = \sqrt{(x_R-x_S)^2+(y_R-y_S)^2} = \sqrt{(0-b)^2+(a-c)^2} = \sqrt{b^2+(a-c)^2}$

Note that your exercise seems to suggest the opposite, i.e.

$\overline{RS} = \sqrt{b^2+(c-a)^2}$

Don't worry: the two numbers are the same. In fact, $a-c$ and $c-a$ are opposite, and opposite numbers are the same when squared (for example, $3^2=(-3)^2=9$)

It had to be so after all: we're simply claiming that the distance between R and S or between S and R is the same..how could it be any different?