Question

An automobile oil-change station is designing a small window sticker to remind its regular customers of their next service milestone. The three vertices of the sticker are shown on the coordinate plane below, where each unit represents one centimeter.



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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.

Answer 1

Answers: The shape is a right triangle; AB = 2 cm; AC = 4 cm.

Reasoning: From the coordinate plane the vertices are A(1,1), B(1,3), and C(5,1). AB is vertical with length |3−1| = 2, AC is horizontal with length |5−1| = 4, and AB ⟂ AC, so the triangle is a right triangle. The hypotenuse BC = sqrt[(5−1)^2 + (1−3)^2] = sqrt(16+4) = sqrt(20) (≈4.472), so the longest edge is neither 5 nor sqrt(29).