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kkurt [141]
3 years ago
13

Shane has a segment with endpoints C(3, 4) and D(11, 3) that is divided by a point E such that CE and DE form a 3:5 ratio. He kn

ows that the distance between the x-coordinates is 8 units. Which of the following fractions will let him find the x-coordinate for point E?
Mathematics
1 answer:
kifflom [539]3 years ago
5 0

Answer:

(6 , 29/8)

Step-by-step explanation:

Let divide the segment into 8 equal parts (since 3 (CE) + 5(ED) = 8)

(11 - 3) / 8 = 8/8 = 1. So each x-segment will be 1 unit

(3 - 4) / 8 = -1/8. So each y-segment shall be -1/8 unit.

CE will represent 3/8 of the relative line.

Ex = 3 + 1 * 3 = 3 + 3 = 6

Ey = 4 + (-1/8) * 3 = 4 - 3/8 = 29/8

(6 , 29/8) is the final answer  

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Answer:

  (5, 2)

Step-by-step explanation:

<h3>understanding the question</h3>

The question is asking you to express the temperature at 5 pm as a pair of graph coordinates.

Doing this requires that you ...

  • read from the graph the temperature at 2 pm
  • read from the graph the temperature at 8 pm
  • figure the temperature halfway between those values
  • express the 5 pm temperature as an ordered pair (hours, °C)

__

<h3>reading the graph</h3>

The description of the graph tells you the horizontal scale is hours after noon, so the temperature at 2 pm will be a point on the graph with an x-coordinate of 2. That point is (2, 7), indicating the temperature at 2 pm is 7 °C.

Likewise, the temperature at 8 pm is shown as the point on the graph with x-coordinate 8. That point is (8, -3), indicating a temperature of -3°C at 8 pm.

<h3>halfway temperature</h3>

The temperature halfway between those values (7 °C and -3 °C) can be found several ways. Perhaps the easiest is to average the values:

  (7 +(-3))/2 = 4/2 = 2

The temperature at 5 pm is 2 °C.

<h3>coordinates</h3>

Coordinates on the graph are ordered pairs of the form (x, y) = (hours, °C). The time 5 pm is 5 hours after noon, so the x-coordinate is 5. The temperature at 5 pm is halfway between the temperatures at 2 and 8 pm, which we have computed to be 2 °C, so the y-coordinate is 2.

The coordinates that represent the temperature at 5 pm are ...

  (5, 2)

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