Question

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1. what is the distance between ( j(-6,-2) ) and ( h(2.5,-2) )?
2. what is the perimeter of rectangle ( j k l m ), with vertices ( j(-1,3), k(2,3), l(2,-5) ), and ( m(-1,-5) )?
3. nikki drew a rectangle with a perimeter of 18 units on a coordinate plane. tof the vertices were ( (4,-3) ) and ( (-1,-3) ). which could be the coordinates of the other two vertices of the rectangle?

a. ( (4,12) ) and ( (-1,12) )
b. ( (-1,1) ) and ( (4,1) )
c. ( (4,6) ) and ( (-1,6) )
d. ( (4,7) ) and ( (-1,7) )
what is the perimeter of the figure
ordinate plane to the

Explanation:

Step1: Find the length of one side

The two given vertices \((4,-3)\) and \((-1,-3)\) have the same \(y -\)coordinate. The distance between them (length of one side of the rectangle) is calculated using the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(y_1 = y_2\): \(d=\vert x_1 - x_2\vert\). So, \(d=\vert4-(-1)\vert=\vert4 + 1\vert=5\) units.

Step2: Use the perimeter formula

The perimeter of a rectangle is \(P = 2(l + w)\), where \(P = 18\) units and \(l = 5\) units. Substitute into the formula: \(18=2(5 + w)\). First, divide both sides by 2: \(\frac{18}{2}=5 + w\), which gives \(9=5 + w\). Then subtract 5 from both sides: \(w=9 - 5=4\) units.

Step3: Check the \(y -\)coordinate difference

For a rectangle, the other two vertices should have a \(y -\)coordinate difference equal to the width. Let the \(y -\)coordinate of the given points be \(y=-3\). If the width \(w = 4\), then the new \(y -\)coordinate \(y'=-3\pm4\). \(y'=-3 + 4=1\) or \(y'=-3-4=-7\).

Answer:

B. \((-1,1)\) and \((4,1)\)