Question

graph the rhombus with vertices (8,7), (8,2), (4,5), and (4,10).

Explanation:

Step1: Identify each vertex

First, we list the vertices of the rhombus: \( A(8, 7) \), \( B(8, 2) \), \( C(4, 5) \), \( D(4, 10) \).

Step2: Plot each point on the coordinate plane

• For point \( A(8, 7) \): Move 8 units along the x - axis (horizontal) and 7 units along the y - axis (vertical) and mark the point.
• For point \( B(8, 2) \): Move 8 units along the x - axis and 2 units along the y - axis and mark the point.
• For point \( C(4, 5) \): Move 4 units along the x - axis and 5 units along the y - axis and mark the point.
• For point \( D(4, 10) \): Move 4 units along the x - axis and 10 units along the y - axis and mark the point.

Step3: Connect the points in order

Connect \( A \) to \( B \), \( B \) to \( C \), \( C \) to \( D \), and \( D \) to \( A \) to form the rhombus. We can verify the sides:

• The distance between \( A(8,7) \) and \( B(8,2) \) is \( |7 - 2|=5 \) (since the x - coordinates are the same, we use the distance formula for vertical lines \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(8 - 8)^2+(2 - 7)^2}=\sqrt{0 + 25} = 5\)).
• The distance between \( B(8,2) \) and \( C(4,5) \): \( d=\sqrt{(4 - 8)^2+(5 - 2)^2}=\sqrt{(- 4)^2+3^2}=\sqrt{16 + 9}=\sqrt{25}=5 \)
• The distance between \( C(4,5) \) and \( D(4,10) \): \( d=\sqrt{(4 - 4)^2+(10 - 5)^2}=\sqrt{0 + 25}=5 \)
• The distance between \( D(4,10) \) and \( A(8,7) \): \( d=\sqrt{(8 - 4)^2+(7 - 10)^2}=\sqrt{16+9}=\sqrt{25} = 5\)

Since all sides are equal, the figure formed by connecting these points in order is a rhombus.

Answer:

To graph the rhombus, plot the points \((8, 7)\), \((8, 2)\), \((4, 5)\), and \((4, 10)\) on the coordinate plane (where the x - axis and y - axis range from 0 to 10) and connect them in order. The graph will show a rhombus with all sides of length 5.