Perpendicular Height
Perpendicular Height - Related Videos
01:29
Perpendicular Lines
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2026
Two lines are perpendicular if they intersect to form a right angle (90 degrees). The relationship between the slopes of perpendicular lines provides an algebraic method for determining whether two lines meet at a right angle. For two nonvertical lines with slopes m1 and m2, the lines are perpendicular if and only if their slopes are negative reciprocals. So, m1m2 = -1. For example, if one line has a slope of 2, a perpendicular line has a slope of -½. Thus, the sign of the slope changes, and...
01:16
Perpendicular-Axis Theorem
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2025
The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body. Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
10:18
Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices
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Cited by 27 •
2017
Multilayer microfluidic devices often involve the fabrication of master molds with complex geometries for functionality. This article presents a complete protocol for multi-step photolithography with valves and variable height features tunable to any application. As a demonstration, we fabricate a microfluidic droplet generator capable of producing hydrogel beads.
11:23
Polydimethylsiloxane-polycarbonate Microfluidic Devices for Cell Migration Studies Under Perpendicular Chemical and Oxygen Gradients
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Cited by 16 •
2017
The control of chemical and oxygen gradients is essential for cell cultures. This paper reports a polydimethylsiloxane-polycarbonate (PDMS-PC) microfluidic device capable of reliably generating combinations of chemical and oxygen gradients for cell migration studies, which can be practically utilized in biological labs without sophisticated instrumentation.
08:24
Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb
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Cited by 5 •
2016
Here, we present a novel protocol to measure positional stability at key events during the sit-to-stand-to-walk using the center-of-pressure to the whole-body-center-of-mass distance. This was derived from the force platform and three-dimensional motion-capture technology. The paradigm is reliable and can be utilized for the assessment of neurologically compromised individuals.
FAQs
Changing the selected base changes the corresponding perpendicular height. In a triangle, each vertex can be paired with the opposite side as a base, so the relevant height is the segment drawn from that vertex to that base at a right angle. These different height-base pairs still describe the same triangle, but they are not interchangeable in an area calculation.
The right angle is the deciding condition because it identifies the direct height rather than an oblique distance to the reference line. Once that perpendicular segment is located, its length can be related to the other sides of the resulting right triangle. This makes perpendicularity useful when a diagram includes several possible segments or angled sides.
Area provides a way to recover an unknown perpendicular height. Starting with A = 1/2bh, multiply both sides by 2 and divide by the selected base b, giving h = 2A/b. The calculation works only when b and h belong to the same base-height pair, so choosing a convenient but unrelated length can produce an incorrect result.
A slanted side or diagonal should not automatically be used as the height. The required segment must connect the chosen reference line with the relevant point while satisfying the right-angle condition. This distinction matters especially when a figure is tilted: its visual orientation may change, but the measurement used as height remains the perpendicular one.
To locate perpendicular height in a diagram, first identify the intended base or reference line. Next, trace or construct the segment from the opposite vertex or point that meets this line at 90 degrees, then measure that segment. For an area problem, substitute this height with its matching base in A = 1/2bh rather than using another visible length.
In coordinate geometry, the same idea becomes a point-to-line distance problem. The point represents the vertex or location whose height is needed, while the line supplies the reference. Perpendicularity determines the relevant segment, and distance principles provide its measurement. This lets geometric height reasoning extend beyond drawn figures to coordinate-based problems.
Perpendicular height is useful whenever a problem asks for an area, compares geometric figures, or involves lengths, angles, and scale. In each case, identify which line or base serves as the reference before measuring. Using the corresponding height keeps comparisons consistent and helps distinguish a genuine change in geometry from a change caused only by scale.