Given the vertices of ∆abc are a (2,5), b (4,6) and c (3,1), find the vertices following each of the transformations from the original vertices:
a. rx-axis

b. ry = 3

c. t< -2,5>

d. t< 3,-6>

e. r(90◦, o)

a)

Reflection over x-axis.

We know that when any point is reflected over the x-axis, then the rule of transformation that is applied is:

               (x,y) → (x,-y)

Hence,

         A (2,5)→ A'(2,-5)

         B (4,6) → B'(4,-6)

and  C (3,1) → C'(3,-1)

b)

 Reflection about the line y=3

We know that any point after reflection is at a fixed distance from the line as it was before reflection.

Hence,

         A (2,5)→ A'(2,1)

         B (4,6) → B'(4,0)

and  C (3,1) → C'(3,5)

c)

T<-2,5>

The rule that is applied to this translation is:

         (x,y) → (x-2,y+5)

Hence,

         A (2,5)→ A'(0,10)

         B (4,6) → B'(2,11)

and  C (3,1) → C'(1,6)

d)

                    T<3,-6>

The rule that is applied to this translation is:

                  (x,y) → (x+3,y-6)

Hence,

         A (2,5)→ A'(5,-1)

         B (4,6) → B'(7,0)

and  C (3,1) → C'(6,-5)

e)

    r(90◦, o)    

It is  a rotation of a point 90 degree clockwise about the origin.

Hence, the rule that describes this transformation is:

           (x,y) → (y,-x)

Hence,

         A (2,5)→ A'(5,-2)

         B (4,6) → B'(6,-4)

and  C (3,1) → C'(1,-3)

d. vertex

step-by-step explanation:

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕