Question

Three points have coordinates A (0 , 7) , B (8 , 3) and C (3k , k)

Answer 1

9514 1404 393

Answer:

  k = 2.8

Step-by-step explanation:

Segments AB and AC are on the same line, so have the same slope. Using the slope formula, we have ...

  m = (y2 -y1)/(x2 -x1)

  (3 -7)/(8 -0) = (k -7)/(3k -0)

Multiplying by 6k gives ...

  -3k = 2(k -7)

  -5k = -14 . . . . . . subtract 2k

  k = 14/5 = 2.8 . . . . divide by -5

Answer 2

Answer:

k=14/5

Problem:

Three points have coordinates A (0 , 7) , B (8 , 3) and C (3k , k)

Find the value of the constant k for which C lies on the line that passes through A and B

Step-by-step explanation:

The slope of a line containing points (a,b) and (c,d) is found by computing (b-d)/(a-c). This is just the change in y divided by the change in x.

The slope of a line containing points (0,7) and (8,3) is (7-3)/(0-8)=4/-8=-1/2.

The slope of a line containing points (0,7) and (3k,k) and (8,3) is still -1/2 because it doesn't matter what two points on a line you use to calculate the slope. The slope will remain the same no matter the pair of points on the line you choose for it's calculation.

So lets pretend the question is now find the point (3k,k) such that a line with slope -1/2 goes through (3k,k) and (0,7).

We want to solve the equation:

(k-7)/(3k-0)=-1/2

Simplify denominator

(k-7)/(3k)=-1/2

Cross multiple

(k-7)(2)=(-1)(3k)

Distribute or multiply

2k-14=-3k

Subtract 2k on both sides

-14=-5k

Divide both sufes by -5

-14/-5=k

Simplifying fraction

14/5=k