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3 years ago

Point (2, 4) is reflected across the x-axis. What are the coordinates of its image?

Mathematics

1 answer:

klio [65]3 years ago

5 0

Answer:

The coordinates of its image are (2, -4)

Step-by-step explanation:

<em>Let us revise the rules of reflection across the axes</em>

If the point (x, y) reflected across the x-axis, then its image is (x, -y), the rule of reflection is rx-axis (x, y) → (x, -y)

If the point (x, y) reflected across the y-axis, then its image is (-x, y), the rule of reflection is ry-axis (x, y) → (-x, y)

∵ The point (2, 4) is reflected across the x-axis

→ By using the first rule above rx-axis (x, y) → (x, -y)

∴ Change the sign of its y-coordinate

∴ Its image is (2, -4)

∴ The coordinates of its image are (2, -4)

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4 years ago

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The distance between the first car and the intersection is $x$ and the distance between the second car and the intersection is $y$ . The distance between the two cars is depicted by $s$ . As we can see, $s$ is the hypotenuse of the right triangle. At the given instance the distances are 8 meters and 6 meters respectively. Thus, by the Pythagorean Theorem the hypotenuse will be:

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Now, we know that at any instant the Pythagorean Theorem holds and so we will have, in general:

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Now, implicitly differentiating the above formula with respect to time, we get:

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This can be further simplified by dividing both the sides by the common factor 2 as:

$s\frac{ds}{st}=x \frac{dx}{dy}+y\frac{dy}{dt}$ .................(Equation 2)

As we can see from the questions and the diagram, $\frac{dx}{dt}=-2 m/s$ and $\frac{dy}{dt}=-9 m/s$ . The negative sign is there because the distances y and x are reducing as the cars approach the intersection.

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