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The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateral
triangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?
triangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?
- a)169/√3
- b)84.5
- c)75√3
- d)169√3/4
- e)225√3/4
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), res...
The formula for the distance between two points (x1, y1) and (x2, y2) is:
One way to understand this formula is to understand that the distance between any two points on the coordinate plane is equal to the hypotenuse of a right triangle whose legs are the difference of the x-values and the difference of the y-values (see figure). The difference of the x-values of P and Q is 5 and the difference of the y-values is 12. The hypotenuse must be 13 because these leg values are part of the known right triangle triple: 5, 12, 13.
We are told that this length (13) is equal to the height of the equilateral triangle XYZ. An equilateral triangle can be cut into two 30-60-90 triangles, where the height of the equilateral triangle is equal to the long leg of each 30-60-90 triangle. We know that the height of XYZ is 13 so the long leg of each 30-60-90 triangle is equal to 13. Using the ratio of the sides of a 30-60-90 triangle (1:√3:2), we can determine that the length of the short leg of each 30-60-90 triangle is equal to 13/√3. The short leg of each 30-60-90 triangle is equal to half of the base of equilateral triangle XYZ. Thus the base of XYZ =2(13√3) = 26√3
The question asks for the area of XYZ, which is equal to 1/2 × base × height:
The correct answer is A.
One way to understand this formula is to understand that the distance between any two points on the coordinate plane is equal to the hypotenuse of a right triangle whose legs are the difference of the x-values and the difference of the y-values (see figure). The difference of the x-values of P and Q is 5 and the difference of the y-values is 12. The hypotenuse must be 13 because these leg values are part of the known right triangle triple: 5, 12, 13.
We are told that this length (13) is equal to the height of the equilateral triangle XYZ. An equilateral triangle can be cut into two 30-60-90 triangles, where the height of the equilateral triangle is equal to the long leg of each 30-60-90 triangle. We know that the height of XYZ is 13 so the long leg of each 30-60-90 triangle is equal to 13. Using the ratio of the sides of a 30-60-90 triangle (1:√3:2), we can determine that the length of the short leg of each 30-60-90 triangle is equal to 13/√3. The short leg of each 30-60-90 triangle is equal to half of the base of equilateral triangle XYZ. Thus the base of XYZ =2(13√3) = 26√3
The question asks for the area of XYZ, which is equal to 1/2 × base × height:
The correct answer is A.
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The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateraltriangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?a)169/√3b)84.5c)75√3d)169√3/4e)225√3/4Correct answer is option 'A'. Can you explain this answer?
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The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateraltriangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?a)169/√3b)84.5c)75√3d)169√3/4e)225√3/4Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateraltriangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?a)169/√3b)84.5c)75√3d)169√3/4e)225√3/4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateraltriangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?a)169/√3b)84.5c)75√3d)169√3/4e)225√3/4Correct answer is option 'A'. Can you explain this answer?.
The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateraltriangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?a)169/√3b)84.5c)75√3d)169√3/4e)225√3/4Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateraltriangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?a)169/√3b)84.5c)75√3d)169√3/4e)225√3/4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateraltriangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?a)169/√3b)84.5c)75√3d)169√3/4e)225√3/4Correct answer is option 'A'. Can you explain this answer?.
Solutions for The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateraltriangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?a)169/√3b)84.5c)75√3d)169√3/4e)225√3/4Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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