Question

If you connected the points in this graph in the order of M-A-H-M, what shape would you have?How do you know?у10286M MX10RE10-H

Answer 1

In this graph the coordinates are:

M(-3, 4), A(5,1), H(-6, -4), T(2, -7)

Let's find the distance between each point using the distance formula:

`d=\text{ }√(()x2-x1)^2+(y2-y1)^2`

For MA:

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

A(5,1) = (x2,y2)

`\begin{gathered} d\text{ = }√((5-(-3))^2+(1-4)^2) \\ \\ =\text{ }√(8^2+(-3)^2) \\ \\ =\text{ }√(64+9) \\ \\ =√(73) \\ \\ =8.54 \end{gathered}`

For AH:

A(5,1)

H(-6,-4)

`\begin{gathered} d\text{ = }√((-6-5)^2+(-4-1)^2) \\ \\ =\text{ }\sqrt{121\text{ + 25}} \\ \\ =\text{ }√(146) \\ \\ =\text{ 12.08} \end{gathered}`

For HT:

H(-6, -4)

T(2, -7)

`\begin{gathered} d=\text{ }√((2-(-6))^2+(-7-(-4))^2) \\ \\ =\text{ }√(64+9) \\ \\ =\text{ }√(73) \\ \\ =\text{ }8.54 \end{gathered}`

For TM:

T(2,-7)

M(-3,4)

`\begin{gathered} d\text{ = }√((-3-2)^2+(4-(-7))^2) \\ \\ =\text{ }√(25+121) \\ \\ =\text{ }√(146) \\ \\ =\text{ 12.08} \end{gathered}`

From the calculations above, we can see the shape is a rectangle because it has two opposite sides are equal.

MA = HT = 8.54

AH = TM = 12.08

ANSWER:

RECTANGLE