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pav-90 [236]
3 years ago
7

Which of the following lines is parallel to x = 7? (2 points) a 3y = 7 b y = 7 c x = y d x = 4

Mathematics
1 answer:
diamong [38]3 years ago
4 0

Answer:

Choice d. l:x = 7 is parallel to the line x = 4.

Step-by-step explanation:

Refer to the diagram attached. (Created with GeoGebra)

The line x = 7 is made of all the points on a cartesian plane that meet the requirement x = 7. In other words, this line consists of points with x-coordinate 7. That includes:

  • (7, -1),
  • (7,0), and
  • (7,1).

That line is perpendicular to the x-axis (the horizontal axis) and intersects the x-axis at the point (7,0).

Now, consider the lines in the choices.

The first line 3y =7 requires only that the y-coordinates of its points be 7/3. This line accepts any x-values. Points on this line include:

  • \displaystyle \left(-1, \frac{7}{3}\right),
  • \displaystyle \left(0, \frac{7}{3}\right), and
  • \displaystyle \left(-1, \frac{7}{3}\right).

As a result, this line is parallel to the y-axis and is perpendicular to the line x = 7.

Similar to the first, the second line y = 7 is also parallel to the y-axis and is perpendicular to the line x = 7.

The third line x = y requires that the x- and y- coordinates of all its points be equal. Points may include:

  • (-1, -1),
  • (0,0), and
  • (1,1).

This line is slant.

The last line x = 4 is similar to the given line x = 7. This line is also perpendicular to the x-axis. The difference is that this line is three units to the left of the line x = 7.

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ankoles [38]

Using the given information, length of QR = 16.6 cm

The area of the trapezium is 304.5 cm²

<h3>Calculating area of a trapezium</h3>

From the question we are to calculate the length of QR and the area of trapezium PQRS

In the given diagram,

Let the midpoint of PS be T

Then, we can write that

|OP|² = |OT|² + |PT|²  (<em>Pythagorean theorem</em>)

|OP| = radius = 13 cm

|PT| = 1/2 × PS = 1/2 × 24 cm = 12 cm

∴ 13² = |OT|² + 12²

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|OT|² = 169 -144

|OT|² = 25

|OT| = √25

|OT| = 5 cm

Also, let the midpoint of QR be U

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|OQ|² = |OU|² + |QU|² (<em>Pythagorean theorem</em>)

|OQ| = radius = 13 cm

From the given information,

The distance of QR from O is twice the distance of PS from O

∴ |OU| = 2 × |OT|= 2 × 5 cm = 10cm

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169 = 10² + |QU|²

|QU|² = 169 -100

|QU|² = 69

|QU| = √69

|QU| = 8.3 cm

Now,

Length of QR = 2 × |QU| = 2 × 8.3 cm

Length of QR = 16.6 cm

b)

Area of the trapezium = 1/2(|QR| + |PS|) × |TU|

Area of the trapezium = 1/2(16.6 + 24) × 15

NOTE: |TU| = |OT| + |OU|

Area of the trapezium = 1/2(40.6) × 15

Area of the trapezium = 20.3 × 15

Area of the trapezium = 304.5 cm²

Hence, the area of the trapezium is 304.5 cm²

Learn more on Calculating area of trapezium here: brainly.com/question/3435635

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