PLEASE HELP Triangle XYZ has its vertices at the following coordinates: X(2, 1) Y(4,-1) Z(1,-3)

Give the coordinates of the image triangle X'Y'Z' after a 90° counterclockwise rotation about the origin.

solved

Step-by-step explanation:

Let , the points are X(x_1,y_1)\ ,Y(x_2,y_2) \ , Z(x_3,y_3)X(x

1

,y

1

) ,Y(x

2

,y

2

) ,Z(x

3

,y

3

) .

When any point ( h , k ) is rotated 90° counterclockwise about the origin the new point produced is ( -k , h).

So , applying same concept in XYZ :

X'(-y_1,x_1)\ ,Y'(-y_2,x_2) \ , Z'(-y_3,x_3)X

′

(−y

1

,x

1

) ,Y

′

(−y

2

,x

2

) ,Z

′

(−y

3

,x

3

) .

Therefore , transformed points are X'(-y_1,x_1)\ ,Y'(-y_2,x_2) \ , Z'(-y_3,x_3)X

′

(−y

1

,x

1

) ,Y

′

(−y

2

,x

2

) ,Z

′

(−y

3

,x

3

) .

Hence , this is the required solution

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b