Two cities are located in the xy-plane at the points A(3,8) and B(6,3). A company wishes to place a factory on a road between the cities at A and B. It is determined
that the company can make the most money if it places the factory exactly halfway
between A and B. However, due to environmental hazards produced by the factory,
it is safe for the people living in A and B only if the factory is located exactly 2/3
of the distance from A going toward B. Find the coordinates of the point where the
factory should be placed to ensure the most ethical outcome. Explain your decision.

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.

d is the only accurate one

step-by-step explanation: