Analytic geometry - practice problems
Analytic geometry, also known as coordinate geometry, is a branch of mathematics that deals with the study of geometric shapes using the techniques of calculus and algebra. It uses a coordinate system to represent geometric shapes and equations, allowing for the use of algebraic methods to solve geometric problems. It is also used to model physical phenomena, such as the motion of objects in space.Number of problems found: 268
- Equation of the line
Find the equation of the line through (1, 2) with slope 3. - The centroid
The centroid of a triangle ABC is at the point (3,3,3). If the coordinates of A and B are (3, –5, 7) and (–1, 7, – 6) respectively, find the coordinates of the point C. - Parallel lines - dist
Find the distance between the parallel lines 3x – 4y +7 = 0 and 3x – 4y + 5 = 0 - Susan 5 Susan has a water tank in his back garden that can hold up to 750L in water. At the start of a rainy day (at 0:00) there is 165L in the tank, and after a heavy day’s rain (at 24:00) there is 201 L in the tank. Assuming that the rain fell consistently duri
- Angle and slope
Find the angle between the x-axis and the line joining the points (3, -1) and (4,-2) . - Equation of a line
Find the equation of a line that passes through (1, 3) and is parallel to the line y = - 2x + 4. - The vertices
The vertices of a triangle are A (-1,3), B (1,-1), and C (5, 1). Find the length of the median through the vertex C.
- Two points M and N are two points on the X-axis and Y-axis, respectively. Point P (3, 2) divides the line segment MN in a ratio of 2:3. Find: (i) the coordinates of M and N (ii) slope of the line MN.
- LS and y-axis intersection In what ratio is the line segment joining P (5, 3) and Q (–5, 3) divided by the y-axis? Also, find the coordinates of the intersection point.
- The coordinates 4
The coordinates of the vertices of ∆ABC are respectively (-4, -2), (6, 2) and (4, 6). Find the centroid G of ∆ABC. - The co-ordinates
The co-ordinates of the point P dividing the line segment joining the points A (1,3) and B (4,6) internally in the ratio 2:1 are - Midpoint 11 Consider the following line segment - start point A=(-4,1), endpoint B=(4,-1). Find the midpoint. Please show your work.
- Vertical axis Find the perpendicular distance of the point A=(5,-7) from the y-axis.
- Collinear lines Points A, B, and C are collinear, and B lies between A and C. If AC = 48, AB = 2x + 2, and BC = 3x + 6, what is BC?
- The endpoints
The endpoints of a segment are (-6,1) and (10,11). What are the coordinates of its midpoint?
- Trigonometric fx
When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ. - X intercept Given: 3y+2x=-6 Calculate the X-intercept.
- Line equation: Line equation: y-3=8/9(x-5) Solve for slope
- Three 237 Three vertices of a rectangle have the coordinates (5, 3), (5, -1), (-1, -1). What are the coordinates of the fourth vertex of the rectangle?
- A triangle 10 A triangle has vertices at (4, 5), (-3, 2), and (-2, 5). What are the coordinates of the vertices of the image after the translation (x, y) arrow-right (x + 3, y - 5)?
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