X2=10-slxaTopic 4: Partitioning a Segment20. Given directed line segment AB, find the coordinates

2 answers
Question:

X2=10-slxa Topic 4: Partitioning a Segment
20. Given directed line segment AB, find the coordinates of P
such that the ratio of AP to AB is 4:5. Plot point P.
A

[tex]X2=10-slxa Topic 4: Partitioning a Segment 20. Given directed line segment AB, find the coordinat[/tex]


Answers

[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]

Step-by-step explanation:

The question is incomplete; However

[tex]A = (-2, -4)[/tex]

[tex]B = (6, 1)[/tex]

Required

Determine coordinates of P

When line segment is divided in ratios, the following formula calculates the coordinates;

[tex]P(x,y) = \{\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\}[/tex]

In this case;

[tex]m:n = 2:1[/tex]

[tex](x_1,y_1) = (-2, -4)[/tex]

[tex](x_2,y_2) = (6, 1)[/tex]

So, the coordinates of P is calculated as thus

[tex]P(x,y) = \{\frac{2 * 6 + 1 * (-2)}{2+1}, \frac{2 * 1 + 1 * (-4)}{2+1}\}[/tex]

[tex]P(x,y) = \{\frac{12 -2}{3}, \frac{2 -4}{3}\}[/tex]

[tex]P(x,y) = \{\frac{10}{3}, \frac{-2}{3}\}[/tex]

Hence, the coordinates of P is

[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]

The point P on line AB such that the ratio of AP to PB is 2:1 is P = (0, 3)

Step-by-step explanation:

The dimension of the graph can be taken as 1 box = 1 unit

Therefore;

The coordinates of the point A = (-2, -7)

The coordinates of the point B = (1, 8)

For the a point P that gives the ratio AP to PB = 2:1 is given as follows;

The fraction of AP to AB = 2/(2 + 1)×AB = 2/3 × AB

Which gives;

The coordinate of the point P = (-2 + 2/3×(1 - (-2)), -7 + 2/3×(8 - (-7)))

P = (0, 3)

Therefore;

The coordinates of P such that the ratio of AP to PB is 2:1 is P = (0, 3).

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