Question

a line segment with endpoints (7.5) and (10.1) is reflected across the line y=-x. which pair of coordinates represents the endpoints of the given segment after the reflection?
a. (-7,5) and (-10,1)
b. (-5,-7) and (-1,-10)
c. (5,7) and (1,10)
d. (7,-5) and (10,-1)

Explanation:

Step1: Recall the reflection rule across \(y = -x\)

When a point \((x,y)\) is reflected across the line \(y=-x\), the transformation rule is \((x,y)\to(-y,-x)\).

Step2: Apply the rule to the first endpoint \((7,5)\)

For the point \((7,5)\), using the rule \((x,y)\to(-y,-x)\), we substitute \(x = 7\) and \(y = 5\). Then \(-y=-5\) and \(-x=-7\), so the new point is \((-5,-7)\).

Step3: Apply the rule to the second endpoint \((10,1)\)

For the point \((10,1)\), using the rule \((x,y)\to(-y,-x)\), we substitute \(x = 10\) and \(y = 1\). Then \(-y=-1\) and \(-x=-10\), so the new point is \((-1,-10)\).

Answer:

B. \((-5,-7)\) and \((-1,-10)\)