Question

1. biking rhea is using a coordinate grid to map out how far she biked from each place in town

how far rhea biked around all the three places in town?
units

1. after the point ( a(-2,4) ) is translated along the vector ( <6,7> ) the image will be

located at (, )

1. which point is the image of ( a(4,3) ) after a reflection in
2. the y - axis?
3. the x - axis?

Explanation:

4)

Step1: Calculate the distance between \(M(-4,2)\) and \(L(-1,6)\)

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1=-4,y_1 = 2,x_2=-1,y_2 = 6\).

$$
LATEXBLOCK0
$$

Step2: Calculate the distance between \(L(-1,6)\) and \(K(2,2)\)

Here \(x_1=-1,y_1 = 6,x_2=2,y_2 = 2\)

$$
LATEXBLOCK1
$$

Step3: Calculate the distance between \(K(2,2)\) and \(M(-4,2)\)

Here \(x_1=2,y_1 = 2,x_2=-4,y_2 = 2\)

$$
LATEXBLOCK2
$$

Step4: Calculate the perimeter

The perimeter \(P=d_{ML}+d_{LK}+d_{KM}\)

$$P = 5+5 + 6=16$$

Step1: Use the translation rule

When a point \((x,y)\) is translated along the vector \(\langle a,b
angle\), the new - point is \((x + a,y + b)\). Given \(x=-2,y = 4,a = 6,b = 7\)

$$
LATEXBLOCK0
$$

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

The rule for reflection over the \(y\) - axis is \((x,y)\to(-x,y)\). Given \(x = 4,y = 3\), then the image is \((-4,3)\)

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

The rule for reflection over the \(x\) - axis is \((x,y)\to(x,-y)\). Given \(x = 4,y = 3\), then the image is \((4,-3)\)

Answer:

\(16\)

5)