Question

Point AAA is at {(6,1)}(6,1)left parenthesis, 6, comma, 1, right parenthesis and point CCC is at {(2,-7)}(2,−7)left parenthesis, 2, comma, minus, 7, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that AB=\dfrac13BCAB= 3 1 ​ BCA, B, equals, start fraction, 1, divided by, 3, end fraction, B, C.

Answer 1

Answer:

5,-1

Step-by-step explanation:

Answer 2

Answer:

The coordinates of B is (3, - 5)

Step-by-step explanation:

A(6, 1)

C(2, -7)

Coordinates of point B such that AB = 1/3 × BC

Hence we have;

$AC = AB + BC = BC + \dfrac{1}{3} \times BC = \dfrac{4}{3} \times BC$

Therefore BC = 3/4 × AC

Hence, AB = 1/3 × BC = 1/3 × 3/4 × AC = 1/4 × AC

AC = √((6 - 2)² + (1 - (-7))²) = √(16 + 64) = √80 = 4·√5

AB = 1/4 × 4·√5 = √5

Therefore;

AB² = (x - 6)² + (y - 1)² = 5

Slope = (1 - (-7))/(6 - 2) = 2

Hence the y coordinate of B = -7 + sin(tan⁻¹(2)) ×√5 = -5

The x coordinate of B = 2 + cos(tan⁻¹(2)) ×√5 = 3

The coordinates of B = (3, - 5)