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Say true or false: Points P(10,,-6),,Q(6,,-4) and C(-8,,3) are

Question

Say true or false:
Points $P (10, - 6), Q (6, - 4)$ and $C (- 8, 3)$ are collinear.

True

False

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Say true or false:

Points

P (10, - 6), Q (6, - 4)

and

C (- 8, 3)

are collinear.

11 mins ago

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11 mins ago

Text solutionVerified

Since the slope of the line with points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

is:

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

We find the slope of the line

PQ

with points

P (10, - 6)

and

Q (6, - 4)

is:

m = \frac{- 4 - ( - 6 )}{6 - 10} = \frac{- 4 + 6}{- 4} = - \frac{1}{2}

Now the slope of the line

QC

with points

Q (6, - 4)

and

C (- 8, 3)

is:

m = \frac{3 - ( - 4 )}{- 8 - 6} = \frac{7}{- 14} = - \frac{1}{2}

Finally the slope of the line

PC

with points

P (10, - 6)

and

C (- 8, 3)

is:

m = \frac{3 - ( - 6 )}{- 8 - 10} = \frac{9}{- 18} = - \frac{1}{2}

Since the slope of

PQ

QC

and

PC

are equal, therefore, the points are collinear.

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Question Text	Say true or false: Points $P (10, - 6), Q (6, - 4)$ and $C (- 8, 3)$ are collinear.
Answer Type	Text solution:1
Upvotes	150

Say true or false:Points P(10,−6),Q(6,−4) and C(−8,3) are collinear.

Text solutionVerified

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Say true or false:
Points $P (10, - 6), Q (6, - 4)$ and $C (- 8, 3)$ are collinear.