Podcast
Questions and Answers
A line segment joins points A(2, 4) and B(6, 8). What are the coordinates of the point that divides AB in the ratio 1:1?
A line segment joins points A(2, 4) and B(6, 8). What are the coordinates of the point that divides AB in the ratio 1:1?
- (8, 12)
- (4, 6) (correct)
- (2, 2)
- (3, 4)
Given the coordinates of the vertices of a triangle are A(0, 0), B(6, 0), and C(0, 8), what is the area of the triangle?
Given the coordinates of the vertices of a triangle are A(0, 0), B(6, 0), and C(0, 8), what is the area of the triangle?
- 8 square units
- 14 square units
- 24 square units (correct)
- 48 square units
Point P(3, y) is 5 units away from the origin. What are the possible values of y?
Point P(3, y) is 5 units away from the origin. What are the possible values of y?
- $\pm 25$
- $\pm 4$ (correct)
- $\pm 16$
- $\pm 2$
A point Q divides the line segment joining A(1, 2) and B(m, n) in the ratio 1:2. If the coordinates of Q are (2, 3), what are the values of m and n?
A point Q divides the line segment joining A(1, 2) and B(m, n) in the ratio 1:2. If the coordinates of Q are (2, 3), what are the values of m and n?
What is the distance between points R(-3, 6) and S(5, -2)?
What is the distance between points R(-3, 6) and S(5, -2)?
If the midpoint of the line segment joining points C(a, b) and D(7, -3) is (4, 2), what are the values of a and b?
If the midpoint of the line segment joining points C(a, b) and D(7, -3) is (4, 2), what are the values of a and b?
The vertices of a triangle are P(1, 2), Q(4, 6), and R(7, 3). What is the length of the median from vertex P to the midpoint of QR?
The vertices of a triangle are P(1, 2), Q(4, 6), and R(7, 3). What is the length of the median from vertex P to the midpoint of QR?
The points A(x, y), B(1, 2), and C(2, 1) form a triangle. If the area of the triangle is 6 square units, which equation must be satisfied?
The points A(x, y), B(1, 2), and C(2, 1) form a triangle. If the area of the triangle is 6 square units, which equation must be satisfied?
Points A(1, 2), B(4, y), and C(6, 3) are collinear. Find the value of y.
Points A(1, 2), B(4, y), and C(6, 3) are collinear. Find the value of y.
Given a triangle with vertices D(0, 4), E(0, 0), and F(3, 0), determine the coordinates of the centroid.
Given a triangle with vertices D(0, 4), E(0, 0), and F(3, 0), determine the coordinates of the centroid.
A circle has its center at the origin and passes through the point (5, 0). Which of the following points lies outside the circle?
A circle has its center at the origin and passes through the point (5, 0). Which of the following points lies outside the circle?
What is the area of a triangle formed by the points (1, 2), (3, 4), and (5, 0)?
What is the area of a triangle formed by the points (1, 2), (3, 4), and (5, 0)?
A line segment joining points P(7, -6) and Q(3, 4) is divided by a point in the ratio 1:2 internally. In which quadrant does this point lie?
A line segment joining points P(7, -6) and Q(3, 4) is divided by a point in the ratio 1:2 internally. In which quadrant does this point lie?
The coordinates of the vertices of a triangle are A(3, 0), B(7, 0), and C(8, 4). What is the area of this triangle?
The coordinates of the vertices of a triangle are A(3, 0), B(7, 0), and C(8, 4). What is the area of this triangle?
The points (-4, 0), (4, 0), and (0, 3) form the vertices of what type of triangle?
The points (-4, 0), (4, 0), and (0, 3) form the vertices of what type of triangle?
Flashcards
Distance Formula
Distance Formula
The distance between two points (P(x_1, y_1)) and (Q(x_2, y_2)) is given by (\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2})
Distance from Origin
Distance from Origin
The distance of a point (P(x, y)) from the origin ((0,0)) is (\sqrt{x^2 + y^2})
Section Formula
Section Formula
The coordinates of the point (P) which divides the line segment joining the points (A(x_1, y_1)) and (B(x_2, y_2)) internally in the ratio (m_1 : m_2) are ((\frac{m_1x_2 + m_2x_1}{m_1+m_2}, \frac{m_1y_2 + m_2y_1}{m_1+m_2}))
Midpoint Formula
Midpoint Formula
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Area of a Triangle
Area of a Triangle
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Condition for Collinearity
Condition for Collinearity
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Study Notes
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Distance Formula: Used to find the distance between two points in a coordinate plane.
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The distance between two points P (x₁, y₁) and Q (x₂, y₂) is given by √((x₂ - x₁)² + (y₂ - y₁)²)
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The distance of a point P (x, y) from the origin (0, 0) is √(x² + y²)
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Section Formula: Determines the coordinates of a point that divides a line segment in a given ratio.
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The coordinates of a point P that divides the line segment joining A (x₁, y₁) and B (x₂, y₂) internally in the ratio m₁ : m₂ are ((m₁x₂ + m₂x₁) / (m₁ + m₂), (m₁y₂ + m₂y₁) / (m₁ + m₂)).
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The coordinates of the midpoint of the line segment joining points P (x₁, y₁) and Q (x₂, y₂) are (((x₁ + x₂) / 2), ((y₁ + y₂) / 2)).
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Area of a Triangle:
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The area of a triangle with vertices A (x₁, y₁), B (x₂, y₂), and C (x₃, y₃) is given by calculating 1/2 [x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)].
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Unless points A, B, and C are collinear the triangle is considered non-zero.
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