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Alecsey [184]
3 years ago
14

Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed fro

m A to B in the ratio of 1:4.
A) (6, 6)
B) (2, 56/5)
C) (24/5, 42/5)
D) (42/5, 24/5)
Mathematics
1 answer:
Bess [88]3 years ago
6 0

So despite what you may think, <u>1:4 is not 1/4 in this situation,</u> but rather it's "1 equal part to 4 equal parts", which is a total of 5 equal parts. <u>In short, they are asking you for the point at the 1/5 mark from A to B.</u>

Firstly, how many units apart is 10 to 2 (the x-coordinates)? That would be 8 units. Multiply 1/5 by 8:

\frac{1}{5}\times \frac{8}{1}=\frac{8}{5}

Next, how many units apart is 4 to 8 (the y-coordinates)? That would be 4 units. Multiply 1/5 by 4:

\frac{1}{5}\times \frac{4}{1}=\frac{4}{5}

Now, since from 10 to 2 you are <u>decreasing</u>, subtract 8/5 from 10:

\frac{10}{1}\times \frac{5}{5}=\frac{50}{5}\\\\\frac{50}{5}-\frac{8}{5}=\frac{42}{5}

42/5 is the x-coordinate.

Now, since from 4 to 8 you are <u>increasing</u>, add 4/5 to 4:

4+\frac{4}{5}=4\frac{4}{5}=\frac{24}{5}

24/5 is the y-coordinate.

<u>Putting it together, the point is (42/5, 24/5), or D.</u>

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Answer:

1. C. 1/4(4) + 1/4(9) (A, 1/4(13), is essentially C simplified (without figuring it out).)

2. G - -4

3. A - -4(-5) + (-4)x

4. J - 1/6x + 1/6y

5. A - 60(10 + 2)

Step-by-step explanation:

1.

1/4(4 + 9) <em>We can distribute 1/4 into 4 and 9.</em>

1/4(4) + 1/4(9) <em>Now while we have our answer, this can be further simplified.</em>

1/4(13) <em>What's on the left is the simplified 2-term equation.</em>

<em>So really, either C or A will be the answer. But due to the format of #3, I put C as my answer. B & D were out because there wasn't any extra multiplication.</em>

2.

-2/5(15 - 5) <em>Subtract 5 from 15 to get 10.</em>

-2/5(10) <em>Multiply -2/5 by 10 to get -20/5</em>

-20/5 <em>Divide -20 by 5 to get -4.</em>

-4, so G is the answer. <em>This was negative, so H & J were out to begin with. F was out as soon as I solved the problem.</em>

3.

-4(-5 + x) <em>Distribute -4 into -5 + x.</em>

-4(-5) + (-4)x, so A is the answer. <em>Don't get tricked! B may look right, but there should be a negative sign in front of the 5, hence why it's incorrect.</em>

4.

1/6(x + y) <em>Distribute 1/6 into x + y.</em>

1/6x + 1/6y, so J is the answer. <em>F & G are already out because you don't multiply the variables by each other. H is also out because there wasn't any multiplication involved other than x + y being multiplied by 1/6.</em>

5.

Only 60(10 + 2) would have worked, so A is the answer. The tickets would have cost 720 dollars (600 + 120). <em>B would have equated to 624 (24 + 600), C would have been 132 (6 * 22), and D would have been 600. (10 * 60).</em>

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Answer:

D

Step-by-step explanation:

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