Using Ratios To Find A Point Along On A Line

This lesson covers:

  1. How to use ratios to find a particular point along a line 
  2. E.g. 'ABC is a straight line. AB : QR is 2 : 5. Point A is at (-7, 5) an C is at (14, -2). Work out the coordinates of point B.'

ABC is a straight line, as shown on the diagram below. AB : BC is 2 : 5.


Work out the coordinates of point B.

(Diagram NOT drawn accurately)

Diagram showing a straight line ABC with coordinates A at -12, -8 and C at 9, 6. The ratio AB to BC is 2 to 5.

(-3, -2)

(-4, -6)

(-6, -4)

0

/

1

ABC is a straight line, as shown on the diagram below. AB : BC is 2 : 3.


Work out the coordinates of point B.

(Diagram NOT drawn accurately)

Diagram showing a straight line ABC with points A at (-10, 8) and C at (5, -2) to find the coordinates of point B using the ratio AB to BC is 2 to 3.

(3, 4)

(4, 6)

(-4, 4)

0

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1

PQR is a straight line, as shown on the diagram below. PQ : QR is 3 : 1.


Work out the coordinates of point Q.

(Diagram NOT drawn accurately)

Diagram showing a straight line PQR with coordinates P (-6, 11) and R (26, -5) and the point Q dividing the line in the ratio 3:1.

Coordinates of Q: (, )

18
-1

0

/

2

Points P (-5, -2) and Q(31, -20) are joined by a straight line.


Point R is a point on PQ. PR : RQ is 7 : 2.


Work out the coordinates of point R.


(, )

23
-16

0

/

2