Question

if point p(-2, -1) is translated 3 units left and 5 units up, then reflected in the x-axis, give the coordinates of the new position. (□, □)
which expression represents the perimeter of the rectangle below?
8x - 43
5x + 12
a. 13x - 31
b. 13x - 55
c. 26x - 62
d. 26x - 124
ch graph:

1. grid
2. domain:

range:

Explanation:

First Sub - Question (Coordinate Transformation)

Step 1: Translate the point left 3 units

To translate a point \((x,y)\) \(a\) units left, we use the rule \((x - a,y)\). For point \(P(-2,-1)\) and \(a = 3\), the new \(x\) - coordinate is \(-2-3=-5\), and the \(y\) - coordinate remains \(-1\) for now. So the point after translation left is \((-5,-1)\).

Step 2: Translate the point up 5 units

To translate a point \((x,y)\) \(b\) units up, we use the rule \((x,y + b)\). For the point \((-5,-1)\) and \(b = 5\), the new \(y\) - coordinate is \(-1 + 5=4\), and the \(x\) - coordinate remains \(-5\). So the point after translation up is \((-5,4)\).

Step 3: Reflect the point over the x - axis

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,-y)\). For the point \((-5,4)\), the new \(y\) - coordinate is \(-4\), and the \(x\) - coordinate remains \(-5\). So the final point is \((-5,-4)\).

The formula for the perimeter \(P\) of a rectangle with length \(l\) and width \(w\) is \(P = 2(l + w)\).
Given that the length \(l=5x + 12\) and the width \(w = 8x-43\).
First, find \(l + w=(5x + 12)+(8x-43)=5x+8x + 12-43=13x-31\).
Then, find the perimeter \(P = 2(13x-31)=26x-62\).

Answer:

\((-5,-4)\)

Second Sub - Question (Perimeter of Rectangle)