# Construct 8

Construct an analytical geometry problem where it is asked to find the vertices of a triangle ABC:

The vertices of this triangle are points A (1,7), B (-5,1) C (5, -11). The said problem should be used the concepts of distance from a point to a line, ratio of a division of a segment by a point, and angle between two lines.

a) find the length of all sides of a given triangle ABC

The vertices of this triangle are points A (1,7), B (-5,1) C (5, -11). The said problem should be used the concepts of distance from a point to a line, ratio of a division of a segment by a point, and angle between two lines.

a) find the length of all sides of a given triangle ABC

### Correct answer:

Tips for related online calculators

Do you want to convert length units?

The Pythagorean theorem is the base for the right triangle calculator.

See also our trigonometric triangle calculator.

The Pythagorean theorem is the base for the right triangle calculator.

See also our trigonometric triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

#### Units of physical quantities:

#### Grade of the word problem:

## Related math problems and questions:

- MO - triangles

On the AB and AC sides of the ABC triangle lies successive points E and F, and on segment EF lie point D. The EF and BC lines are parallel. It is true this ratio FD:DE = AE:EB = 2:1. The area of the ABC triangle is 27 hectares, and line segments EF, AD, a - Points on line segment

Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB. - Sides of the triangle

The sides of the triangle ABC have a length of 4 cm, 5 cm, and 7 cm. Construct triangle A'B'C', similar to triangle ABC, which has a circumference of 12 cm. - Half-planes 36831

The line p and the two inner points of one of the half-planes determined by the line p are given. Find point X on the line p so that the sum of its distances from points A and B is the smallest. - Construct 13581

The vertices of the triangle ABC lie on the circle k. The circle k is divided into three parts in a ratio of 1:2:3. Construct this triangle. - Distance between 2 points

Find the distance between the points (7, -9), (-1, -9) - Rhombus construction

Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it, touching all sides. - ABCDEFGHIJKL 8426

The given is a regular hexagonal prism ABCDEFGHIJKL, which has all edges of the same length. Find the degree of the angle formed by the lines BK and CL in degrees. - Vertices of a right triangle

Show that the points D(2,1), E(4,0), and F(5,7) are vertices of a right triangle. - MG=7x-15,

Length of lines MG = 7x-15 and FG = 33 Point M is the midpoint of FG. Find the unknown x. - (instructions: 3314

Find the distance of the parallels, which equations are: x = 3-4t, y = 2 + t and x = -4t, y = 1 + t (instructions: select a point on one line and find its distance from the other line) - Triangles 2157

Construct the vertices C of all triangles ABC, if given side AB, height vb on side b and length of line tc on side c. Build all the solutions. Mark the vertices C1, C2,. .. - Rhombus MATH

Construct a rhombus M A T H with diagonal MT=4cm, angle MAT=120° - Line segment

For the line segment whose endpoints are L[-1, 13] and M[18, 2], find the x and y value for the point located 4 over 7, the distance from L to M. - Points OPQ

Point P is on line segment OQ. Given OP = 6, OQ = 4x - 3, and PQ = 3x, find the numerical length of OQ. - Slope form

Find the equation of a line given the point X(8, 1) and slope -2.8. Arrange your answer in the form y = ax + b, where a and b are the constants. - Shortest walk

An ant is crawling around this cube. The cube is made of wire. Each side of the cube is 3 inches long. (Those sides are called edges.) Points A and B are vertices of the cube. What is the least distance the ant would have to crawl if it starts from point