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frozen [14]
4 years ago
13

Point AAA is at {(1, 5)}(1,5)left parenthesis, 1, comma, 5, right parenthesis and point CCC is at {(-5,-7)}(−5,−7)left parenthes

is, minus, 5, comma, minus, 7, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that ACACA, C is 666 times as long as ABABA, B.
Mathematics
1 answer:
Novay_Z [31]4 years ago
8 0

Answer:

(0, 3)

Step-by-step explanation:

If a point O(x, y) divides a line XY in the ratio n:m with X\ at\ (x_1,y_1)\ Y\ at\ (x_2,y_2), the coordinates of O is:

x=\frac{n}{n+m} (x_2-x_1)+x_1\\\\y=\frac{n}{n+m} (y_2-y_1)+y_1

AC is 6 times AB, this means that point B, divides line AC in the ratio 1:5. Given A at (1,5) and C at (-5, -7)

Let us assume B to be at (x, y), hence:

x=\frac{1}{1+5}(-5-1)+ 1=\frac{1}{6}(-6)+1 =0\\\\y=\frac{1}{1+5}(-7-5)+5=\frac{1}{6} (-12)+5=3

Therefore the location of B is (0, 3)

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Step-by-step explanation:

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Step-by-step explanation:

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