Question

1. s(3,4), t(3,1), u(-2,1), v(-2,4) reflection across the x - axis. transformation rule: (x,y)→____ image preimage coordinates (x,y)

Explanation:

Step1: Recall the reflection rule over the x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\).

Step2: Apply the rule to each point

• For point \(S(3,4)\):

Using the rule \((x,y)\to(x, - y)\), we substitute \(x = 3\) and \(y = 4\). So the image is \((3,-4)\).

• For point \(T(3,1)\):

Substitute \(x = 3\) and \(y = 1\) into the rule \((x,y)\to(x, - y)\). The image is \((3,-1)\).

• For point \(U(-2,1)\):

Substitute \(x=-2\) and \(y = 1\) into the rule \((x,y)\to(x, - y)\). The image is \((-2,-1)\).

• For point \(V(-2,4)\):

Substitute \(x=-2\) and \(y = 4\) into the rule \((x,y)\to(x, - y)\). The image is \((-2,-4)\).

Answer:

Preimage Coordinates \((x,y)\)	Transformation Rule: \((x,y)\to(x, - y)\)	Image
\(T(3,1)\)		\(T'(3,-1)\)
\(U(-2,1)\)		\(U'(-2,-1)\)
\(V(-2,4)\)		\(V'(-2,-4)\)