Question

P(-4,5) and Q(6,4) are two points. Find the co ordinates of the point R on PQ such that PR=3QR​

Answer 1

Step-by-step explanation:

Coordinates of P and Q are (2,-1) and(-3,4).

If PQ is hypotaneouse of a triangle then it's base and perpendicular are given by

{2-(-3)}=5 and

4-(-1)=5

so it is a rt. angled triangle with angles 90, 45, 45 and

(PQ)^2 =25+25=50

so PQ=root(50)

Therefore PR=2/5PQ=2 root (50)/5

so (PR)^2 =4*50/25=8

andPR=2 root2

if PR also forms a rt. angled then

it's base=PR cos45

=2 root(2)/root(2)

=2

and perpendicular is

PR sin45=2

because Coordinates of P are (2,-1)

Therefore coordinates of R

x=2-2=0 and

y=2-1=1

so coordinates of R are (0, 1)

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Answer 2

Answer:

P(-4,5) and Q(6,4) are two points. Find the co ordinates of the point R on PQ such that PR=3QR