A triangle has vertices at (−2, −2), (−2, −5), and (−4, −5). The triangle is translated 2 units to the right and rotated 90° clockwise about the origin. What are the coordinates of its image? ( , ), ( , ), ( , ) → ( , ), ( , ), ( , ),

Step-by-step explanation:

translated (shifted) 2 units to the right (positive x direction) creates the points

(-2 + 2, -2) = (0, -2)

(-2 + 2, -5) = (0, -5)

(-4 + 2, -5) = (-2, -5)

and now we rotate these points 90° clockwise around the origin.

that means a positive x turns into a negative y, a negative y into a negative x, a negative x into a positive y, and a positive y into a positive x.

and a 0 just trades places.

therefore,

(0, -2) becomes (-2, 0)

(0, -5) becomes (-5, 0)

(-2, -5) becomes (-5, 2)

so, overall

(-2, -2) becomes (-2, 0)

(-2, -5) becomes (-5, 0)

(-4, -5) becomes (-5, 2)

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

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.