Question

What are two ways that you can find the length and width of the rectangle of (-4,-3) and (2,1).

Answer 1

They give us the point of the diagonal of a rectangle

The first way is count

-First, we count the number of units horizontally until the other point

-Second we count the number of units vertically until the other point

we do the same for the other point

and we found the rectangle

To find the length we count the units from (-4,-3) until (2,-3)

length is equal to 6

to find the width we count the units from (-4,-3) until (-4,1)

width is equal to 3

The second way is using the formula for distance between two points

`\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \end{gathered}`

for the length

(-4,-3) =(x1,y1)

(2,-3)=(x2,y2)

we substitute the values

`\begin{gathered} d=\sqrt[]{(-3+3)^2+(-4-2)^2} \\ d=\sqrt[]{0+36} \\ d=\sqrt[]{36} \\ d=6 \end{gathered}`

the length is 6

then for the width

(-4,-3)=(x1,y1)

(-4,1)=(x2,y2)

we substitute the values

`\begin{gathered} d=\sqrt[]{(1+3)^2+(-4+4)^2} \\ d=\sqrt[]{4^2+0} \\ d=\sqrt[]{16} \\ d=4 \end{gathered}`

the width is 4