Question

exit ticket seal the deal!
△ abc has vertices a (1, -3), b (3, -2), and c (0, -1). give the coordinates of abc after each set of transformations.

1. translate △ abc 2 units left followed by a reflection in the x - axis.

step 1: translate all coordinates 2 left step 2: reflect all coordinates in the x - axis

1. rotate △ abc 90° counterclockwise about the origin followed by a translation up 2 units.

step 1: rotate all coordinates 90° ccw step 2: translate all coordinates 2 units up

Explanation:

Problem 1

Step1: Translate 2 units left

To translate a point \((x,y)\) 2 units left, we use the rule \((x - 2,y)\).
For \(A(1,-3)\): \(A_1=(1 - 2,-3)=(-1,-3)\)
For \(B(3,-2)\): \(B_1=(3 - 2,-2)=(1,-2)\)
For \(C(0,-1)\): \(C_1=(0 - 2,-1)=(-2,-1)\)

Step2: Reflect over x - axis

To reflect a point \((x,y)\) over the \(x\) - axis, we use the rule \((x,-y)\).
For \(A_1(-1,-3)\): \(A''=(-1,-(-3))=(-1,3)\)
For \(B_1(1,-2)\): \(B''=(1,-(-2))=(1,2)\)
For \(C_1(-2,-1)\): \(C''=(-2,-(-1))=(-2,1)\)

Problem 2

Step1: Rotate \(90^{\circ}\) counterclockwise about origin

The rule for rotating a point \((x,y)\) \(90^{\circ}\) counterclockwise about the origin is \((-y,x)\).
For \(A(1,-3)\): \(A_1=(-(-3),1)=(3,1)\)
For \(B(3,-2)\): \(B_1=(-(-2),3)=(2,3)\)
For \(C(0,-1)\): \(C_1=(-(-1),0)=(1,0)\)

Step2: Translate 2 units up

To translate a point \((x,y)\) 2 units up, we use the rule \((x,y + 2)\).
For \(A_1(3,1)\): \(A''=(3,1 + 2)=(3,3)\)
For \(B_1(2,3)\): \(B''=(2,3 + 2)=(2,5)\)
For \(C_1(1,0)\): \(C''=(1,0 + 2)=(1,2)\)

Answer:

s:

1. \(A''(-1,3)\), \(B''(1,2)\), \(C''(-2,1)\)
2. \(A''(3,3)\), \(B''(2,5)\), \(C''(1,2)\)