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kondaur [170]
3 years ago
12

A, B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:4.

Mathematics
2 answers:
schepotkina [342]3 years ago
7 0

Let point C has coordinates (x_C,y_C). Consider vectors

\overrightarrow{AB}=(x_B-x_A,y_B-y_A)=(8-9,6-9)=(-1,-3),\\ \\\overrightarrow{BC}=(x_C-x_B,y_C-y_B)=(x_C-8,y_C-6).

Since the ratio AB to BC is 1:4, you have that

\dfrac{-1}{x_C-8}=\dfrac{1}{4}\quad \text{and}\quad \dfrac{-3}{y_C-6}=\dfrac{1}{4}.

Find x_C and y_C:

x_C-8=-4,\\ \\x_C=-4+8=4,\\ \\y_C-6=-3\cdot 4=-12,\\ \\y_C=-12+6=-6.

Answer: C(4,-6)

andreev551 [17]3 years ago
3 0

Answer:

The coordinates of C are (4, -6)

Step-by-step explanation:

By the section formula,

The coordinate of a point that divides a line segment joining (x_1, y_1) and (x_2, y_2) in the ratio of m : n are,

(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})

Here,

x_1=9, y_1=9, m = 1, n = 4

Also,

\frac{mx_2+nx_1}{m+n}=8

\frac{x_2+36}{1+4}=8

x_2+36=40

x_2=4

\frac{my_2+ny_1}{m+n}=6

\frac{y_2+36}{5}=6

y_2+36=30

y_2=-6

Hence, the coordinates of C are (4, -6)

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