A Triangle with Vertices at (X1, Y1), (X2, Y2), and (X3

question 84

Multiple Choice

A triangle with vertices at (x1, y1) , (x2, y2) , and (x3, y3) has area equal to the absolute value of D, where $$D = \frac { 1 } { 2 } \left| \begin{array} { l l l } x _ { 1 } & y _ { 1 } & 1 \\x _ { 2 } & y _ { 2 } & 1 \\x _ { 3 } & y _ { 3 } & 1\end{array} \right|$$ Find the area of the triangle having vertices at P, Q, and R.
- $P ( 0 , - 4 ) , Q ( 0,5 ) , R ( 5,1 )$

• A) 3
• B) 45
• C) \(\frac { 45 } { 2 }\)
• D) 0

Recognize the moral significance of autonomy and rationality in humans.

Apply Kantian ethics to evaluate moral dilemmas and ethical decisions.

Differentiate between categorical and hypothetical imperatives.

Grasp the principle of universality and its application to Kantian ethics.

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Definitions:

Weighted Mean

An average in which each data point contributes to the final mean with a weight that reflects its importance or frequency.

Central Tendency

A statistical measure that identifies a single value as representative of an entire distribution, with the mean, median, and mode being common examples.

Variability

A statistical measure of the dispersion of data points in a data series around the mean.

Central Tendency

A statistical measure that identifies a single value as representative of an entire distribution of data, commonly the mean, median, or mode.