Question

1 point a (-2,-10) is reflected over the x - axis. write the coordinates of a. (a) (2,-10) (b) (-2,-10) (c) (2,10) (d) (-2,10) 2 point d (2,4) is rotated 180° about the origin. what is the coordinate of d? (a) (-4,2) (b) (-2,-4) (c) (4,-2) (d) (-4,-2) 3. point x(-3,-2) is translated 3 to the right and up 2, then reflected over the x - axis. what is the coordinate of x? (a) (0,2) (b) (-2,0) (c) (0,-2) (d) (2,0)

Explanation:

1. Reflection over the \(x -\)axis

Step1: Recall the reflection rule

When a point \((x,y)\) is reflected over the \(x -\)axis, the rule is \((x,y)\to(x, - y)\).
For point \(A(-2,-10)\), \(x=-2\) and \(y = - 10\).

Step2: Apply the rule

Using the rule \((x,y)\to(x, - y)\), we substitute \(x=-2\) and \(y=-10\). So the new \(y -\)coordinate is \(-(-10)=10\) and \(x\) remains \(-2\). The coordinates of \(A'\) are \((-2,10)\)

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin, the rule is \((x,y)\to(-x,-y)\)
For point \(D(2,4)\), \(x = 2\) and \(y=4\)

Step2: Apply the rule

Substitute \(x = 2\) and \(y = 4\) into \((-x,-y)\). We get \(-x=-2\) and \(-y=-4\). So the coordinates of \(D'\) are \((-2,-4)\)

Step1: Translation

When a point \((x,y)\) is translated \(a\) units to the right and \(b\) units up, the rule is \((x,y)\to(x + a,y + b)\). Here \(a = 3\) and \(b=2\), for point \(X(-3,-2)\), \(x=-3\) and \(y=-2\). After translation: \(x=-3 + 3=0\) and \(y=-2+2 = 0\), so the point is \((0,0)\)

Step2: Reflection over the \(x -\)axis

Using the reflection rule \((x,y)\to(x,-y)\) for the point \((0,0)\). Substituting \(x = 0\) and \(y = 0\), we get \((0,0)\) (since \(-0=0\))

Answer:

\((d)\) \((-2,10)\)

2. Rotation of \(180^{\circ}\) about the origin