Question

1. define the terms below. sketch an example.

a. translation
b. reflection
c. rotation

1. define the terms below. sketch an example.

a. corresponding angle
b. alternate exterior angles
c. alternate interior angle

1. (5.6) what are the coordinates of ( j) and ( k) after ( jk) is reflected across the ( y)-axis?

a. (j(-3,1),k(-1,4))
b. (j(-3,6),k(-1, - 1))
c. (j(3,-1),k(1,-4))
d. (j(3,1),k(1,4))

1. (5.8ac) a student graphed triangle ( abc) on a coordinate - plane, as shown to the right.

after a translation, the location of vertex ( a) is ((-1,-1)). what ordered pair describes the location of point ( b) after the triangle is translated?
a. ((-8,-5))
b. ((-8,5))
c. ((-5,-2))
d. ((-5,2))

Explanation:

1.

a. Translation: A translation is a transformation that moves every point of a figure or a space by the same distance in a given direction. For example, if we have a triangle and we move it 3 units to the right and 2 units up, all its vertices will be shifted by these amounts. Sketch: Draw a simple triangle, then draw the same - sized triangle a few units away in a particular direction.
b. Reflection: A reflection is a transformation that flips a figure over a line called the line of reflection. For example, reflecting a triangle over the y - axis will change the sign of the x - coordinates of its vertices. Sketch: Draw a triangle and its mirror - image across a vertical line.
c. Rotation: A rotation is a transformation that turns a figure around a fixed point called the center of rotation. For example, rotating a triangle 90 degrees counter - clockwise around a point will change the orientation of the triangle. Sketch: Draw a triangle and then draw the triangle rotated around a point inside or outside it.

2.

a. Corresponding angles: When two parallel lines are cut by a transversal, corresponding angles are in the same relative position at each intersection. For example, if we have two parallel lines \(l_1\) and \(l_2\) cut by a transversal \(t\), the top - left angle at the intersection of \(l_1\) and \(t\) and the top - left angle at the intersection of \(l_2\) and \(t\) are corresponding angles. Sketch: Draw two parallel lines and a transversal, and label the corresponding angles.
b. Alternate exterior angles: When two parallel lines are cut by a transversal, alternate exterior angles are the non - adjacent angles that lie outside the two parallel lines and on opposite sides of the transversal. For example, if we have parallel lines \(m\) and \(n\) cut by a transversal \(k\), the angles that are outside \(m\) and \(n\) and on opposite sides of \(k\) are alternate exterior angles. Sketch: Draw two parallel lines and a transversal, and label the alternate exterior angles.
c. Alternate interior angles: When two parallel lines are cut by a transversal, alternate interior angles are the non - adjacent angles that lie between the two parallel lines and on opposite sides of the transversal. For example, if we have parallel lines \(p\) and \(q\) cut by a transversal \(r\), the angles that are between \(p\) and \(q\) and on opposite sides of \(r\) are alternate interior angles. Sketch: Draw two parallel lines and a transversal, and label the alternate interior angles.

3.

The rule for reflecting a point \((x,y)\) across the y - axis is \((x,y)\to(-x,y)\). If we assume the original coordinates of \(J\) and \(K\) are \((x_1,y_1)\) and \((x_2,y_2)\) respectively, after reflection across the y - axis, the new coordinates will be \((-x_1,y_1)\) and \((-x_2,y_2)\). Looking at the options, when we reflect points across the y - axis, the y - coordinate remains the same and the x - coordinate changes sign.

Answer:

A. \(J'(- 3,1),K'(-1,4)\)

4.