Question

1. (3 points) the image of point f reflected in the line y = x is located at f(-7, 1). what are the coordinates of point f?

f( ____ , ____ )

1. (1 point) the image of j(-2, 9) after being translated along the vector (-1, -3) is

a. j(3, -6)
b. j(-3, 6)
c. j(-7, 12)

1. (2 points) which set of coordinates models the image of the triangle after a translation along the vector (2, -9)?

a. m(-5, 16), n(-2, 13), p(0, 15)
b. m(-1, -2), n(2, -5), p(4, -3)
c. m(-5, -21), n(-2, -5), p(0, -3)

Explanation:

Question 4

Step1: Reflection over \(y = x\) rule

When a point \((x,y)\) is reflected over the line \(y=x\), the transformation rule is \((x,y)\to(y,x)\). Let the coordinates of point \(F\) be \((x,y)\). Given \(F'(-7,1)\), using the reflection rule \(y = x\) (if \(F(x,y)\) is reflected over \(y=x\) to get \(F'(y,x)\)).

Step2: Find \(x\) and \(y\)

We have \(y=-7\) and \(x = 1\) (since for reflection over \(y=x\), if \(F'(a,b)\) is the image of \(F\), then \(F=(b,a)\))

Step1: Translation rule

For a point \((x,y)\) translated along the vector \((a,b)\), the new - point \((x',y')=(x + a,y + b)\). Here \(x=-2\), \(y = 9\), \(a=-1\), \(b=-3\)

Step2: Calculate \(x'\) and \(y'\)

\(x'=-2+(-1)=-3\) and \(y'=9+(-3)=6\)

Step1: Translation rule

For a point \((x,y)\) translated along the vector \((a,b)\), the new - point \((x',y')=(x + a,y + b)\). Here \(a = 2\), \(b=-9\)
For point \(M(-3,7)\): \(x'=-3 + 2=-1\), \(y'=7-9=-2\), so \(M'(-1,-2)\)
For point \(N(0,4)\): \(x'=0 + 2=2\), \(y'=4-9=-5\), so \(N'(2,-5)\)
For point \(P(2,6)\): \(x'=2 + 2=4\), \(y'=6-9=-3\), so \(P'(4,-3)\)

Answer:

\(F(1,-7)\)

Question 5