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The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate plane below are 2 vertices of triangle RST, which has a right angle at S. Which of the following could be the third vertex, T ?
- a)(5, 7)
- b)(5, -5)
- c)(4, 6)
- d)(4, 9)
- e)(4, 9/2)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate pla...
Because there is a right angle at S, the point T will lie along the line through S that is perpendicular to the segment RS. To solve this problem, find the equation for the line through S that is perpendicular to the segment RS and try each answer choice to find one that lies on the line. Since the line is perpendicular to segment RS, it will have a slope that is the opposite reciprocal of the slope of RS. Since slope is rise/run, the slope of RS is 
The slope of a line perpendicular to that is -4. Because a point and the slope of the line are known, the point-slope form of the equation can be utilized. A line through point (h, -k) with slope m has equation y - k = m(x - h). Thus the line through S (6,-3) that is perpendicular to the segment RS has equation y - 3 = -4(x - 6). Distributing and adding like terms, the result is y = -4x + 27. Of the answer choices, only the point (5, 7) falls on the line.
The slope of a line perpendicular to that is -4. Because a point and the slope of the line are known, the point-slope form of the equation can be utilized. A line through point (h, -k) with slope m has equation y - k = m(x - h). Thus the line through S (6,-3) that is perpendicular to the segment RS has equation y - 3 = -4(x - 6). Distributing and adding like terms, the result is y = -4x + 27. Of the answer choices, only the point (5, 7) falls on the line.Most Upvoted Answer
The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate pla...
Because there is a right angle at S, the point T will lie along the line through S that is perpendicular to the segment RS. To solve this problem, find the equation for the line through S that is perpendicular to the segment RS and try each answer choice to find one that lies on the line. Since the line is perpendicular to segment RS, it will have a slope that is the opposite reciprocal of the slope of RS. Since slope is rise/run, the slope of RS is The slope of a line perpendicular to that is -4. Because a point and the slope of the line are known, the point-slope form of the equation can be utilized. A line through point (h, -k) with slope m has equation y - k = m(x - h). Thus the line through S (6,-3) that is perpendicular to the segment RS has equation y - 3 = -4(x - 6). Distributing and adding like terms, the result is y = -4x + 27. Of the answer choices, only the point (5, 7) falls on the line.
The slope of a line perpendicular to that is -4. Because a point and the slope of the line are known, the point-slope form of the equation can be utilized. A line through point (h, -k) with slope m has equation y - k = m(x - h). Thus the line through S (6,-3) that is perpendicular to the segment RS has equation y - 3 = -4(x - 6). Distributing and adding like terms, the result is y = -4x + 27. Of the answer choices, only the point (5, 7) falls on the line.Community Answer
The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate pla...
Because there is a right angle at S, the point T will lie along the line through S that is perpendicular to the segment RS. To solve this problem, find the equation for the line through S that is perpendicular to the segment RS and try each answer choice to find one that lies on the line. Since the line is perpendicular to segment RS, it will have a slope that is the opposite reciprocal of the slope of RS. Since slope is rise/run, the slope of RS is The slope of a line perpendicular to that is -4. Because a point and the slope of the line are known, the point-slope form of the equation can be utilized. A line through point (h, -k) with slope m has equation y - k = m(x - h). Thus the line through S (6,-3) that is perpendicular to the segment RS has equation y - 3 = -4(x - 6). Distributing and adding like terms, the result is y = -4x + 27. Of the answer choices, only the point (5, 7) falls on the line.
The slope of a line perpendicular to that is -4. Because a point and the slope of the line are known, the point-slope form of the equation can be utilized. A line through point (h, -k) with slope m has equation y - k = m(x - h). Thus the line through S (6,-3) that is perpendicular to the segment RS has equation y - 3 = -4(x - 6). Distributing and adding like terms, the result is y = -4x + 27. Of the answer choices, only the point (5, 7) falls on the line.
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The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate plane below are 2 vertices of triangle RST, which has a right angle at S. Which of the following could be the third vertex, T ?a)(5, 7)b)(5, -5)c)(4, 6)d)(4, 9)e)(4, 9/2)Correct answer is option 'A'. Can you explain this answer?
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The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate plane below are 2 vertices of triangle RST, which has a right angle at S. Which of the following could be the third vertex, T ?a)(5, 7)b)(5, -5)c)(4, 6)d)(4, 9)e)(4, 9/2)Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate plane below are 2 vertices of triangle RST, which has a right angle at S. Which of the following could be the third vertex, T ?a)(5, 7)b)(5, -5)c)(4, 6)d)(4, 9)e)(4, 9/2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The points R (2, 2) and S (6, 3) in the standard (x, y) coordinate plane below are 2 vertices of triangle RST, which has a right angle at S. Which of the following could be the third vertex, T ?a)(5, 7)b)(5, -5)c)(4, 6)d)(4, 9)e)(4, 9/2)Correct answer is option 'A'. Can you explain this answer?.
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