5.2.3 Coordinates, PT3 Focus Practice


Question 7:
Diagram shows a straight line PQ on a Cartesian plane.

 
Calculate the length, in unit, of PQ.

Solution:

PS = 15 – 3 = 12 units 
SQ = 8 – 3 = 5 units 

By Pythagoras’ theorem,
PQ= PS2 + SQ2
 = 122+ 52
PQ = √169
  = 13 units


Question 8:
The diagram shows an isosceles triangle STU.

 
Given that ST = 5 units, the coordinates of point are

Solution:

 
For an isosceles triangle STU, M is the midpoint of straight line TU.
xcoordinate of M = 2+4 2 =1
Point M = (1, 0)
 
MT = 4 – 1 = 3 units 
By Pythagoras’ theorem,
SM= ST2MT2
= 52 – 32
= 25 – 9
= 16
SM = √16
= 4
Therefore, point S = (1, 4).

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