Question

The following points are plotted on the coordinate plane 81-5159 C(129) D00, Consider the distance between the origin and each point. Determine whether each point is less than 15 units greater than 15 units, or exactly 15 units from the origin Write the letter of each point in the correct column in the table. Less than 15 units Exactly 15 units Greater than 15 units UPLOAD YOUR WORKIN CANVAS

Answer 1

The distance between two points is given by:

`d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}}`

where A(x1,y1) and B(x2,y2).

In this case we are going to use the points given in the problem and the origin, which have coordinates O(0,0). Then the distances are:

`\begin{gathered} d(O,A)=\sqrt[]{(11-0)^2+(-6-0)^2} \\ =\sqrt[]{121+36} \\ =\sqrt[]{157} \\ \approx12.53 \end{gathered}`
`\begin{gathered} d(O,B)=\sqrt[]{(-5-0)^2+(15-0)^2} \\ =\sqrt[]{25+225} \\ =\sqrt[]{250} \\ \approx15.81 \end{gathered}`
`\begin{gathered} d(O,C)=\sqrt[]{(12-0)^2+(-9-0)^2} \\ =\sqrt[]{144+81} \\ =\sqrt[]{225} \\ =15 \end{gathered}`
`\begin{gathered} d(O,D)=\sqrt[]{(10-0)^2+(4-0)^2} \\ =\sqrt[]{100+16} \\ =\sqrt[]{116} \\ \approx10.77 \end{gathered}`
`\begin{gathered} d(O,E)=\sqrt[]{(-8-0)^2+(-14-0)^2} \\ =\sqrt[]{64+196} \\ =\sqrt[]{260} \\ \approx16.12 \end{gathered}`

From the distances above we conclude that:

Less than 15 units:

A

D

Exactly 15 units:

C

Greater than 15 units:

B

E