8.2 Coordinates, PT3 Focus Practice


8.2 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 P(–4, 6) and Q(20, –1).

Solution
:
Distance of P Q = ( 4 20 ) 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,
PQ2= 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 Sare

Solution
:
 
For an isosceles triangle STU, M is the midpoint of straight line TU.
x coordinate of M = 2 + 4 2 = 1
Point M = (1, 0)
 
MT = 4 – 1 = 3 units 
By Pythagoras’ theorem,
SM2= ST2MT2
= 52 – 32
= 25 – 9
= 16
SM = √16
   = 4
Therefore, point S = (1, 4).

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