Question

for what value of p, are the points (-3,9) , (2,p) and (4,-5) collinear ?

Answer 1

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Answer 2

Answer:

The value of p is -1 with the points (-3,9), (2,p) and (4,-5) being collinear.

Step-by-step explanation:

Step 1:

Given data:

Let A(-3,9) ,B (2,p) and C (4,-5)  are collinear

To Find the Value of X:

The Angle ABC area=0

Step 2:

1/2|x1(y2-y3+x2(y3-y1)+x3(y1-y2)|=0  

The points to be collinear:

=|(-3)[p-(-5)]+2[-5-9]+4[9-p]|=0  (substitute the values x1=-3,y1=9,x2=2,y2=p,x3=4,y3=-5)

Step 3:

=|(-3)[p+5]-2(5+9)+4(9-p)|=0  

=-3p-15-10-18+36-4p=0    (therefore -15-10-18+36=-7)

Step 4:

=-7p-43+36=0    (Subtract the value (-43+36=7))

=-7p-7=0

Step 5:

=-7p=7

p=-7/7  (Cancelling the values -7/7=-1)

p=-1