Question

which statements are true? select three that apply
the measure of the longest edge of the sticker is 5 centimeters
the design in the coordinate plane indicates that the shape of the sticker is a right triangle
the height of the sticker, represented by the distance between a and b, is 2 centimeters.
the width of the sticker, represented by the distance between a and c, is 4 centimeters.
the measure of the longest edge of the sticker is √29 centimeters.

Explanation:

Step1: Find coordinates of points

Assume \(A=(1,2)\), \(B=(1,4)\), \(C=(5,2)\)

Step2: Calculate distances between points

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
For \(AB\): \(x_1 = 1,y_1 = 2,x_2 = 1,y_2 = 4\), \(d_{AB}=\sqrt{(1 - 1)^2+(4 - 2)^2}=\sqrt{0 + 4}=2\)
For \(AC\): \(x_1 = 1,y_1 = 2,x_2 = 5,y_2 = 2\), \(d_{AC}=\sqrt{(5 - 1)^2+(2 - 2)^2}=\sqrt{16+0}=4\)
For \(BC\): \(x_1 = 1,y_1 = 4,x_2 = 5,y_2 = 2\), \(d_{BC}=\sqrt{(5 - 1)^2+(2 - 4)^2}=\sqrt{16 + 4}=\sqrt{20}=2\sqrt{5}\approx4.47\)

Step3: Check right - triangle property

Slope of \(AB\): Since \(x\) - coordinates are the same (\(x = 1\)), slope is undefined.
Slope of \(AC\): \(m_{AC}=\frac{2 - 2}{5 - 1}=0\)
Since the product of the slopes of \(AB\) and \(AC\) is \(0\times\) (undefined) and \(AB\perp AC\), it is a right - triangle.

Answer:

The design in the coordinate plane indicates that the shape of the sticker is a right triangle.
The height of the sticker, represented by the distance between A and B, is 2 centimeters.
The width of the sticker, represented by the distance between A and C, is 4 centimeters.