Question

help please

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)

Answer 1

Given the vertices of a triangle as A(2, 5), B(4, 6) and C(3, 1).

a.) A transformation, R_x-axis means that the vertices of the rectangle were reflected across the x-axis.
When a point on the coordinate axis is refrected across the x-axis, the sign of the y-coordinate of the point changes.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule R_x-axis are A'(2, -5), B'(4, -6), C'(3, -1)

b.) A transformation, R_y = 3 means that the vertices of the rectangle were reflected across the line y = 3.
When a point on the coordinate axis is refrected across the a horizontal line, the distance of the point from the line is equal to the distance of the image of the point from the line.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule are A'(2, 1), B'(4, 0), C'(3, 5)

c.) A transformation, T<-2, 5> means that the vertices of the rectangle were shifted 2 units to the left and 5 units up.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<-2, 5> are A'(0, 10), B'(2, 11), C'(1, 6).

d.) A transformation, T<3, -6> means that the vertices of the rectangle were shifted 3 units to the right and 6 units down.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<3, -6> are A'(5, -1), B'(7, 0), C'(6, -5).

e.) A transformation, r(90°, o) means that the vertices of the rectangle were rotated 90° to the right about the origin.
When a point on the coordinate axis is rotated about the origin b 90°, the quadrant of the point changes to the right with the x-value and the y-value of the point interchanging.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule r(90°, o) are A'(5, -2), B'(6, -4), C'(1, -3)

Answer 2

Answer with explanation:

Vertices of ∆ABC are A (2,5), B (4,6) and C (3,1).

Plotting the points on coordinate plane

a.→ $R_{x}$

   We have to find vertices of image , that is ΔA'B'C' when ∆ABC is reflected across x axis.

The Distance from each of the vertices of ∆ABC from X axis will be same as Perpendicular distance from each of vertices of ∆A'B'C' from X axis.

Result is shown in the image 1.

b.→$R_{y}=3$

We have to find the image of vertices of triangle through line, y=3.

The Distance from each of the vertices of ∆ABC from line,y=3  will be same as Perpendicular distance from each of vertices of ∆A'B'C' from line, y=3.

Result is shown in the image 2.

c. →T(-2,5)

Translation of vertices of triangle ABC by 2 units left and 5 units up.

$A(2,5)_{-2,5} \rightarrow (2-2,5+5)\rightarrow (0,10)\\\\B(4,6)_{-2,5} \rightarrow (4-2,6+5)\rightarrow (2,11),\\\\C(3,1)_{-2,5} \rightarrow (3-2,1+5)\rightarrow (1,6)$

d.→T(3,-6)

Translation of vertices of triangle ABC by 3 units right and 6 units left.

$A(2,5)_{3,-6} \rightarrow (2+3,5-6)\rightarrow (5,-1)\\\\B(4,6)_{3,-6} \rightarrow (4+3,6-6)\rightarrow (7,0),\\\\C(3,1)_{3,-6} \rightarrow (3+3,1-6)\rightarrow (6,-5)$

e.→Rotation by 90° with respect to Origin

When rotated in clockwise direction ,vertices of ΔABC changes by the rule ,that is (x,y)→(y,-x) and in anticlockwise direction ,(x,y)→(-y,x).

In clockwise direction

A(2,5)→A"(5,-2)

B(4,6)→B"(6,-4)

C(3,1)→C"(1,-3)

In Anti clockwise direction

A(2,5)→A'(-5,2)

B(4,6)→B'(-6,4)

C(3,1)→C'(-1,3)

Image is depicted below.