You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-165 m, 59 m). the x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (bx and -70), then (-20 and cy), then (-60 and -70). what are (a) component bx and (b) component cy? what are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement?

(a) The sum of all the x displacements is

And we know that the final x position is -165. We deduce

(b) Similarly, we sum all the y displacements and we impose them to be equal to the final displacement:

(c) The magnitude of the overall displacement is given by

(d) The angle is given by

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.