Perpendicularity Math Example 2

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Example 2

medium
Determine whether triangle A(0,0)A(0,0), B(4,0)B(4,0), C(4,3)C(4,3) is a right triangle, and if so identify the right angle vertex.

Solution

  1. 1
    Step 1: Slope of ABAB: horizontal, mAB=0m_{AB} = 0. Slope of BCBC: vertical (undefined, since xx is constant at 44). Slope of ACAC: mAC=3/4m_{AC} = 3/4.
  2. 2
    Step 2: A horizontal and a vertical line are perpendicular (they form a 90°90° angle). Therefore AB⊥BCAB \perp BC.
  3. 3
    Step 3: The right angle is at vertex B(4,0)B(4,0), the common endpoint of the two perpendicular sides.

Answer

Yes, right triangle with the right angle at B(4,0)B(4, 0).
To find right angles in a coordinate triangle, compute the slopes of each side and check for perpendicularity (m1m2=−1m_1 m_2 = -1, or one horizontal and one vertical). Here ABAB is horizontal and BCBC is vertical, meeting at 90°90° at BB.

About Perpendicularity

Lines, segments, or planes that intersect at exactly a right angle of 90°90° to each other.

Learn more about Perpendicularity →

More Perpendicularity Examples

Example 1 easy

Line [formula]. Write the equation of a line [formula] perpendicular to [formula] that passes throug

Example 3 easy

Line [formula] passes through [formula] with slope [formula]. Write the equation of the line perpend

Example 4 hard

Find the foot of the perpendicular from point [formula] to the line [formula].

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