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mathematics UK Year 10 Mathematics (KS4)

Solved problems for the chapter:

Coordinates

View the theory »

The distance between two points in a plane for KS4

1. Distance between two points

2. Distance Properties

3. Midpoint between two points

4. Forum

View the theory »

Equation of a straight line for KS4

0.1. The Gradient-Intercept Form:

0.2. The General Form:

0.3. The intercept form of the equation of a line:

1. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:coordinates/3575/

Example 1.

Calculate the coordinates of the bisectors of the lines.

Example 2.

Given points and , calculate the:

distance between points Aand B,
distance of point A from the coordinate origin,
coordinates of the midpoint of line AB.

The coordinates of the midpoint of line AB is R (-2, 1) and coordinates of point A is (6,4). Calculate the coordinates of the point B .

In the room we have the following elements, as shown in the diagram:

Check the correctness of the following statements:

Calculate the distance between the point and , and leave the result in surd form.

Write the relationship between the geometric elements in the diagram:

line p,
line q,
plane and
plane .

Without rounding, calculate the distance between points:

In the room we have the following elements, as shown in the diagram:

Check the correctness of the following statements:

Calculate the coordinates of the bisectors of the lines.

10.

Without rounding, calculate the distance between points:

11.

Without rounding, calculate the distance between points:

12.

Obtain the distance between G and H if

13.

The end points of the line are given. Find the ordinate of the point , which is considered to be 10 units away from the point .

14.

Is the triangle with vertices , and equilateral?

15.

The midpoint of the line is the point . Calculate the coordinates of the point if .

16.

Given a triangle ABC with vertices A (-3,4), B (2,1) and C (1,7).

a) Calculate the length of the median produced on side AB.

b) Calculate the coordinates of the centre of gravity.

17.

Let the points and be the coordinates of the endpoints of a line segment. Calculate the length of this line segment and the coordinates of its midpoint.

18.

The vertices of triangle ABC are: , , .

Is the triangle ABC isosceles?
Calculate the coordinates of the median produced on side AB.
Calculate the height of the median produced on side AB.

19.

Let the points and be the coordinates of the endpoints of a line segment. Calculate the length of this line segment and the coordinates of its midpoint.

20.

Prove that the following points are vertices of a parallelogram:

, , and

21.

In the given coordinate system, draw a line segment with the endpoints . Hence, calculate its length.

22.

Points and are the furthest on a circle. What is the radius of the circle?

23.

The coordinates of the vertices of the parallelogram are: , , and . What is the length of the shorter diagonal?

24.

Points , and are the vertices of an isosceles triangle. Calculate the height of the triangle to the side .

25.

The points and are given. The point divides the line in the ratio . What are the coordinates of the point ?

26.

Use the formula to determine the coordinates of the midpoint of line AB with the vertices and and also prove that the point bisects the line .

27.

The vertices of the rectangle , , and are given.

Graphically solve for the vertex .
Calculate the length of the diagonal of the rectangle .
Calculate the area of the rectangle .

28.

The point is the midpoint of line , which has one end at point . Determine the coordinates of the second point which is point A..

29.

The following points are the vertices of the parallelogram:

, , and

Determine the coordinates of the vertex D.
Calculate the coordinates of the intersection of the diagonals of the parallelogram.
Determine the coordinates of the point T, which lies on the line AB and divides it in the ratio .

30.

Points , and are given. Calculate the value of if .

31.

The coordinates of the endpoints of the line segment, are: and . Find the abscissa of point if the line measures Write down the two possible solutions.