Question

1. what is the distance between j(-6, -2) and h(2.5, -2)?
2. what is the perimeter of rectangle jklm, 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 of the vertices were (4, -3) and (-1, -3). which co

other two vertices of the rectangle?

Explanation:

\(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(J(-6,-2)\) and \(H(2.5,-2)\), \(x_1=-6,y_1 = - 2,x_2=2.5,y_2=-2\).

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Step2: Calculate the perimeter of the rectangle

For rectangle \(JKLM\) with \(J(-1,3)\), \(K(2,3)\), \(L(2,-5)\), \(M(-1,-5)\).
The length \(JK\): Using the distance formula with \(J(-1,3)\) and \(K(2,3)\), \(d_{JK}=\sqrt{(2-(-1))^2+(3 - 3)^2}=\sqrt{(3)^2+0}=3\).
The width \(KL\): Using the distance formula with \(K(2,3)\) and \(L(2,-5)\), \(d_{KL}=\sqrt{(2 - 2)^2+(-5 - 3)^2}=\sqrt{0+(-8)^2}=8\).
The perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l = 8\) and \(w = 3\).

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Step3: Analyze the vertices of the rectangle

For a rectangle, opposite sides are equal. Given two vertices \((4,-3)\) and \((-1,-3)\). The distance between them is \(\sqrt{(4-(-1))^2+(-3+3)^2}=5\).
If we assume the rectangle has sides parallel to the axes. Another pair of vertices can be found by changing the \(y\) - coordinate (if the side is vertical) or \(x\) - coordinate (if the side is horizontal).
If we consider a vertical side: from \((4,-3)\), if we move up or down. Let's assume the height of the rectangle. If we assume the rectangle has length \(5\) (distance between \((4,-3)\) and \((-1,-3)\)) and let the other side length be \(h\).
If we consider the point \((4,y)\) and \((-1,y)\) (parallel to the \(x\) - axis side). If we assume the rectangle has a side of length \(6\) (for example, if perimeter - related logic, but since perimeter of the whole rectangle with two given vertices as a side of length \(5\) and assume the other side \(h\), perimeter \(P=2(5 + h)\). If we assume \(h = 6\) (not given in the problem, but based on rectangle properties).
The other two vertices: If we move up \(6\) units from \((4,-3)\) we get \((4,3)\) and from \((-1,-3)\) we get \((-1,3)\)

Answer:

1. The distance between \(J(-6,-2)\) and \(H(2.5,-2)\) is \(8.5\).
2. The perimeter of rectangle \(JKLM\) is \(22\).
3. Two other vertices of the rectangle could be \((4,3)\) and \((-1,3)\) (assuming a vertical side of length \(6\) relative to the side between \((4,-3)\) and \((-1,-3)\) which has length \(5\))