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elena-s [515]
3 years ago
13

line AB has endpoints A (-3, 1) and B (4, 5), find the coordinates of point p on directed line segment AB that partitions AB in

the ratio of 5:2
Mathematics
2 answers:
Margarita [4]3 years ago
8 0
<h3>Given</h3>

A(-3, 1), B(4, 5)

<h3>Find</h3>

coordinates of P on AB such that AP/PB = 5/2

<h3>Solution</h3>

AP/PB = 5/2 . . . . . desired result

2AP = 5PB . . . . . . multiply by 2PB

2(P-A) = 5(B-P) . . . meaning of the above

2P -2A = 5B -5P . . eliminate parentheses

7P = 2A +5B . . . . . collect P terms

P = (2A +5B)/7 . . . .divide by the coefficient of P

P = (2(-3, 1) +5(4, 5))/7 . . . . substitute the given points

P = (-6+20, 2+25)/7 . . . . . . simplify

P = (2, 3 6/7)

Lynna [10]3 years ago
5 0

Firstly, let's look at this ratio 5:2. Despite what you may think, <em>5:2 is not equal to 5/2,</em> but rather it is equal to "5 equal parts to 2 equal parts", which make up a total of 7 equal parts. <u>In short, they want us to place point P at 5/7 of line AB.</u>

Firstly, how far is -3 to 4 (the x coordinates)? That would be 7 units. Multiply 5/7 by 7:

\frac{5}{7}\times \frac{7}{1}=\frac{35}{7}=5

Next, how far is 1 from 5 (the y-coordinates)? That would be 4 units. Multiply 5/7 by 4:

\frac{5}{7}\times \frac{4}{1}=\frac{20}{7}=2\frac{6}{7}

Next, since from -3 to 4 you are <em>increasing</em>, add 5 to -3, which gets you a sum of 2. <u>2 is the x-coordinate of point P</u>.

Next, since from 1 to 5 you are <em>increasing,</em> add 2 6/7 to 1, which gets you a sum of 3 6/7. <u>3 6/7 is the y coordinate of point P.</u>

<u>Putting it together, point P is at (2,3\frac{6}{7})</u>

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