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5.2.4 Coordinates, PT3 Focus Practice


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=13R=(13,1)



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