All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
3681
What is the slope of the line given by the equation 2x + y = 5?
Answer:
-2
Step 1: Convert the linear equation into the slope-intercept form, y = mx + c. Step 2: Isolate y: y = -2x + 5. Step 3: The coefficient of x is the slope, which is -2.
3682
What is the slope of a perfectly vertical line?
Answer:
Undefined
Step 1: A vertical line has the same x-value for any y-value (x1 = x2). Step 2: In the slope formula m = (y2 - y1) / (x2 - x1), the denominator becomes 0. Step 3: Division by zero is undefined, so the slope is undefined.
3683
Calculate the slope of the line passing through (0, 5) and (5, 0).
Answer:
-1
Step 1: Use the slope formula m = (y2 - y1) / (x2 - x1). Step 2: Insert the coordinates: m = (0 - 5) / (5 - 0). Step 3: Simplify: m = -5 / 5 = -1.
3684
What is the slope of the line joining the points (-1, -1) and (2, 2)?
Answer:
1
Step 1: Apply the slope formula m = (y2 - y1) / (x2 - x1). Step 2: Substitute: m = (2 - (-1)) / (2 - (-1)). Step 3: Simplify: m = (2 + 1) / (2 + 1) = 3 / 3 = 1.
3685
Find the slope of the line passing through the points (1, 2) and (3, 6).
Answer:
2
Step 1: Use the slope formula m = (y2 - y1) / (x2 - x1). Step 2: Substitute the given values: m = (6 - 2) / (3 - 1). Step 3: Compute the result: m = 4 / 2 = 2.
3686
What is the slope of the line passing through the points (0, 0) and (3, 3)?
Answer:
1
Step 1: Use the slope formula m = (y2 - y1) / (x2 - x1). Step 2: Substitute the coordinates: m = (3 - 0) / (3 - 0). Step 3: Simplify: m = 3 / 3 = 1.
3687
What is the center of a circle if the endpoints of its diameter are (-4, 2) and (4, -2)?
Answer:
(0, 0)
Step 1: The center of a circle is the midpoint of its diameter. Step 2: Use the midpoint formula for (-4, 2) and (4, -2). Step 3: x = (-4 + 4)/2 = 0; y = (2 + (-2))/2 = 0. The center is the origin (0, 0).
3688
For the points A(-2, 4) and B(4, -2), what is the midpoint of segment AB?
Answer:
(1, 1)
Step 1: Use the midpoint formula. Step 2: x-coordinate = (-2 + 4)/2 = 2/2 = 1. Step 3: y-coordinate = (4 + (-2))/2 = 2/2 = 1. The midpoint is (1, 1).
3689
The midpoint of the line segment joining the origin (0, 0) and the point (10, 10) is:
Answer:
(5, 5)
Step 1: Apply the midpoint formula to points (0,0) and (10,10). Step 2: x = (0 + 10)/2 = 5. Step 3: y = (0 + 10)/2 = 5. The midpoint is (5, 5).
3690
If (x, y) is the midpoint of the line segment joining (2, 3) and (4, 7), what is the value of x + y?
Answer:
8
Step 1: Find the midpoint coordinates. x = (2 + 4)/2 = 3. y = (3 + 7)/2 = 5. Step 2: The midpoint is (3, 5). Step 3: Calculate the sum: x + y = 3 + 5 = 8.