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vichka [17]
3 years ago
7

Given directed line segment PR below, find the coordinates of Q on PR

Mathematics
1 answer:
g100num [7]3 years ago
5 0

Answer:

(\frac{4}{3},-3)

Step-by-step explanation:

The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at (x_1,y_1) and B(x_2,y_2) is given by the formula:

x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1

From the graph, the location of the point is P(2, 5), R(1, -7). Let point Q be (x, y) which divides PR in ratio 2:1. Coordinates of point Q is at:

x=\frac{a}{a+b}(x_2-x_1)+x_1=\frac{2}{2+1}(1-2)+2=\frac{2}{3}(-1)+2=\frac{4}{3}   \\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1=\frac{2}{2+1}(-7-5)+5= \frac{2}{3}(-12)+5=-3

Point Q is at (\frac{4}{3},-3)

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For the given sentences, the algebraic expressions are:

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<h3>How to get the algebraic expressions?</h3>

For the first statement:

A 3-digit number, where the tens digit is c, can be written as:

N = 100*a + 10*c + b

Then the hundreds digit is a, and here we know that is 3 less than the tens digit, then:

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The ones digit is b, here we know that it is 0, then b = 0.

Replacing that in our number we get:

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That is the algebraic expression.

b) A two-digit number can be written as:

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N = b*10 + a = b*10 + 2b = 12*b

N = 12*b

That is the algebraic expression.

If you want to learn more about algebraic expressions:

brainly.com/question/4541471

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