Question

in which quadrant will the triangle be located after this series of transformations? Does the size of the triangle change after the series of transformations? 1. Translate (x, y) → (x + 1, y + 2) 2. R (origin, 90° clockwise) 3. Translate (x, y) → (x + 2, y - 3)

Answer 1

Answer:

A) It will remain in the first quadrant.

B) There is no size of the triangle will change.

Step-by-step explanation:

Given : Triangle change after the series of transformations.

To find :

A) In which quadrant will the triangle be located after this series of transformations?

B) Does the size of the triangle change after the series of transformations?

Solution :

1)  Translate (x, y) → (x + 1, y + 2)

In this situation the x coordinate will be translated 1 units horizontally and 2 units vertically but the triangle will remain in the first quadrant.

2) Rotation (origin, 90° clockwise)

When we rotate it with the help of angle 90°, it will also remain in the first quadrant.

3) Translate (x, y) → (x + 2, y - 3)

In this situation the x coordinate will be translated 2 units horizontally and 3 units vertically.

A) It will remain in the first quadrant.

B) There is no size of the triangle will change.

Answer 2

The triangle will remains in the first quadrant in all the above condition and the size of triangle is also same because only position of the triangle changes.

Further explanation:

Given:

Triangle is located in the first Quadrant.

To find:

(a) The Quadrant in which the triangle is located after series of transformation at given condition.

(b) The size of triangle after the series of transformation at given condition.

Calculation:

1. Transformation is $(x,y)\rightarrow(x+1,y+2)$.

As per the above transformation the $x$ coordinate of the triangle is shifted horizontally by $1$ unit and the $y$ coordinate is shifted vertically upwards by $2$ units.

The triangle will remain in the first quadrant.

2. Rotated $90^{\circ}$ clockwise.

The triangle will be in the first quadrant and the size of triangle is also not change.  Due to rotation the orientation of the triangle will change.

3. Transformation is $(x,y)\rightarrow(x+2,y-3)$.

As per the above transformation the $x$ coordinate of the triangle is shifted horizontally by $2$ units and the $y$ coordinate is shifted vertically downwards by $3$ units.

The triangle will remains in the first quadrant.

Therefore, the triangle will remains in the first quadrant in all the above condition and the size of triangle is also same because only position of the triangle changes.

Learn more:

1. A problem on triangle https://brainly.com/question/7437053

2. A problem on transformation of triangle https://brainly.com/question/2992432

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Function

Keywords: Equations, Triangle, Transformation, Translate, first quadrant, size, x coordinate, y coordinate, shifted position, rotate clockwise, series of transformation, shifting, quadrant.