134k views
3 votes
Point D (2,6) after a transformation is at D' (5,0). What type of transformation occurred?

a. Translation
b. Rotation
c. Reflection
d. Dilation

User Imad
by
8.6k points

1 Answer

2 votes

Final answer:

The line perpendicular to the given equation has a negative reciprocal slope of -3. Using the point (-1, -1) and slope -3, we find the perpendicular line to be y = -3x - 4. None of the answer choices provided perfectly match this equation.

Step-by-step explanation:

To find the equation of the line perpendicular to the given equation 3y = 4x + 6 - 3x + 6, which simplifies to 3y = x + 12 or y = (1/3)x + 4, we first identify the slope of the original line. This line has a slope of 1/3. The slope of a line that is perpendicular to this line would be the negative reciprocal of 1/3, which is -3.The next step is to use the slope-point form y - y1 = m(x - x1), where (x1, y1) is the point through which the new line passes, and m is the slope of the new line. Substituting the point (-1, -1) and the slope -3, we get y - (-1) = -3(x - (-1)), which simplifies to y + 1 = -3x - 3Finding the y-intercept, we set x to 0 in the equation and solve for y: y + 1 = -3(0) - 3; y = -4. The equation of the perpendicular line in slope-intercept form y = mx + b is y = -3x - 4.The correct choice that matches this equation is A) y = -4x - 1, however, there seems to be a discrepancy.

The coefficient before x is correct (-4 matches -3x), but the constant term does not match what we derived (-1 instead of -4). Therefore, none of the choices provided perfectly match the correct equation of the perpendicular line y = -3x - 4.To find the equation of a line perpendicular to the given equation, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given equation is 3y = 4x + 6 - 3x + 6. We can rewrite this equation as 3y = x + 12. The slope of this line is 1/3. The negative reciprocal of 1/3 is -3.Now, we have the slope of the perpendicular line. To find its equation, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.Given the point (-1, -1), we can substitute these values into the equation and the slope -3 to get: y - (-1) = -3(x - (-1)). Simplifying this equation gives y + 1 = -3x - 3. Rearranging the terms gives y = -3x - 4.Therefore, the equation of the line perpendicular to the given equation and passes through the point (-1, -1) is y = -3x - 4.

User ThatMSG
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories