# 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: 256

- 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)?

- Y-intercept 2

What is the y-intercept of 4x + 8y =16? Write coordinates of x0, y0 of that y-intercept. - Slope of the line

What is the slope of the line passing through two points (-3,5) and (2, -1) - A boy 5

A boy starts at A and walks 3km east to B. He then walks 4km north to C. Find the bearing of C from A. - Coordinates - rectangle

Find the perimeter of the rectangle with vertices A(1,4), B (1,0 ), C (4,0), D (4,4 ) - A function

A function follows the rule "y is 3 less than half of x". Express y as a function of x in the form of an equation.

Do you have homework that you need help solving? Ask a question, and we will try to solve it.