8.2.1 Coordinates, PT3 Focus Practice


8.2.1 Coordinates, PT3 Focus Practice

Question 1
:
In diagram below, Q is the midpoint of the straight line PR.
The value of is

Solution
:
2 + m 2 = 5 2 + m = 10 m = 8


Question 2:
In diagram below, P and Q are points on a Cartesian plane.
 
 
If M is the midpoint of PQ, then the coordinates of M are

Solution:
P( 4,8 ), Q( 6,2 ) Coordinates of M =( 4+6 2 , 8+( 2 ) 2 ) =( 1,3 )


Question 3:
Find the distance between (–4, 6) and (20, –1).

Solution
:
Distance of PQ = ( 420 ) 2 + [ 6( 1 ) ] 2 = ( 24 ) 2 + 7 2 = 576+49 = 625 =25 units


Question 4:
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 5:
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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