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25 May 2022, 06:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
23% (02:30) correct
77%
(02:27)
wrong
based on 43
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On the xy-plane, what is the area of a right triangle, one side of which is defined by the two points having the (x,y) coordinates (2,3) and (24,0)?
(1) The triangle crosses the y-axis at exactly two points.
(2) The y-coordinate of two of the triangle’s three vertices is 0.
Are You Up For the Challenge: 700 Level Questions
(1) The triangle crosses the y-axis at exactly two points.
(2) The y-coordinate of two of the triangle’s three vertices is 0.
Are You Up For the Challenge: 700 Level Questions
Updated on: 02 Jun 2022, 05:25
Originally posted by Pankaj0901 on 25 May 2022, 10:48.
Last edited by Pankaj0901 on 02 Jun 2022, 05:25, edited 3 times in total.
Last edited by Pankaj0901 on 02 Jun 2022, 05:25, edited 3 times in total.
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Answer E
This is how I solved:
(1) The triangle crosses the y-axis at exactly two points.
Consider that the two given points lie on the circumference of the circle, and there is a third point on the left part of the x-y coordinate plane (quadrants II and III), in order to ensure that the triangle touches the y-axis at 2 points. We know that the diameter subtends 90 degrees at any point on the circumference of the circle. Now, you can easily visualize that one of the given points, (2,3) or (24,0), can be diametrically opposite to the another point that lies on the left part (quadrant II and III) of the coordinate plane, and the other given point will be the vertex forming right angle. So, there can be infinitely many such right-angled triangles whose two sides cross the y-axis at two points.
Not sufficient
(2) The y-coordinate of two of the triangle’s three vertices is 0.
There can be two ways:
1. the third vertex is at (2,0).
2. (2,3) is the right-angled and the third vertex lies somewhere on the x-axis.
Not Sufficient
Answer E
This is how I solved:
(1) The triangle crosses the y-axis at exactly two points.
Consider that the two given points lie on the circumference of the circle, and there is a third point on the left part of the x-y coordinate plane (quadrants II and III), in order to ensure that the triangle touches the y-axis at 2 points. We know that the diameter subtends 90 degrees at any point on the circumference of the circle. Now, you can easily visualize that one of the given points, (2,3) or (24,0), can be diametrically opposite to the another point that lies on the left part (quadrant II and III) of the coordinate plane, and the other given point will be the vertex forming right angle. So, there can be infinitely many such right-angled triangles whose two sides cross the y-axis at two points.
Not sufficient
(2) The y-coordinate of two of the triangle’s three vertices is 0.
There can be two ways:
1. the third vertex is at (2,0).
2. (2,3) is the right-angled and the third vertex lies somewhere on the x-axis.
Not Sufficient
Answer E
Bunuel
On the xy-plane, what is the area of a right triangle, one side of which is defined by the two points having the (x,y) coordinates (2,3) and (24,0)?
(1) The triangle crosses the y-axis at exactly two points.
(2) The y-coordinate of two of the triangle’s three vertices is 0.
Are You Up For the Challenge: 700 Level Questions
(1) The triangle crosses the y-axis at exactly two points.
(2) The y-coordinate of two of the triangle’s three vertices is 0.
Are You Up For the Challenge: 700 Level Questions
02 Jun 2022, 13:27
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How is it option e when we can find out the 3rd coordinate using both the statements 1 and 2 since it is crossing y axis at 2 points, one of which being the origin. Someone please explain
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