8.2.2 Coordinates, PT3 Focus Practice


Question 6:
The point M (x, 4), is the midpoint of the line joining straight line Q (-2, -3) and R (14, y).
The value of x and y are

Solution:

x=2+142x=122x=64=3+y28=3+yy=11


Question 7:
In diagram below, PQR is a right-angled triangle. The sides QR and PQ are parallel to the y-axis and the x-axis respectively. The length of QR = 6 units.

Given that M is the midpoint of PR, then the coordinates of M are

Solution:
x-coordinate of R = 3
y-coordinate of R = 1 + 6 = 7
R = (3, 7)

P(1,1),R(3,7)Coordinates of M=(1+32,1+72)=(2,4)


Question 8:
Given points (–2, 8) and (10, 8), find the length of PQ.

Solution:
Length of PQ=[10(2)]2+(88)2=(14)2+0=14 units


Question 9:
In diagram below, ABC is an isosceles triangle.

Find
(a) the value of k,
(b) the length of BC.

Solution:
(a)For an isosceles triangle, ycoordinate of C is the midpoint of straight line AB.2+k2=32+k=6  k=8(b)B=(2,8)BC=[10(2)]2+[3(8)]2 =122+52 =13 units


Question 10:
Diagram below shows a rhombus PQRS drawn on a Cartesian plane. PS is parallel to x-axis.

Given the perimeter of PQRS is 40 units, find the coordinates of point R.

Solution:
All sides of rhombus have the same length,therefore length of each side=404=10 unitsPQ=10(9x1)2+(7(1))2=1028118x1+x12+64=100x1218x1+45=0(x13)(x115)=0x1=3,15x1=3Q=(3,1),R=(x2,1)QR=10(x23)2+[1(1)]2=102x226x2+9+0=100x226x291=0(x2+7)(x213)=0x2=7,13x2=13