On the x-y coordinate grid, if points P, Q, and R make a triangle (not shown), what is the area of the triangle?(1)Point Q lies on the x-axis 6 units from point P.(2)Point R is 5 units away from the x-axisa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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On the x-y coordinate grid, if points P, Q, and R make a triangle (not shown), what is the area of the triangle?

(1) Point Q lies on the x-axis 6 units from point P.

(2) Point R is 5 units away from the x-axis

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'C'. Can you explain this answer?

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On the x-y coordinate grid, if points P, Q, and R make a triangle (not...

Steps 1 & 2: Understand Question and Draw Inferences

To find the area of the triangle, you need the base and the height.

With point P on the x-axis, knowing points Q and R will help you find the base and height.

Step 3: Analyze Statement 1

(1) Point Q lies on the x-axis 6 units from point P.

This gives you the base of the triangle. Whether point Q is left or right of point P, the triangle base is 6. However, you still need the height.

Statement 1 is not sufficient.

Step 4: Analyze Statement 2

(2) Point R is 5 units away from the x-axis

If the base of the triangle is on the x-axis, then knowing point R is 5 away gives you a height of 5. However, with this statement alone, you don’t have the base, and you don’t know whether the base is on the x-axis..

Statement 2 is not sufficient.

Step 5: Analyze Both Statements Together (if needed)

From statement 1, you know that the base is on the x-axis and that it has a length of 6.

From statement 2, because the base is on the x axis, you know the height is 5.

These are all you need to calculate the area of the triangle. The left-right placement of points Q and R don’t affect the area calculation:

Area = ½ * 6 * 5 = 15

Answer: Option (C)

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On the x-y coordinate grid, if points P, Q, and R make a triangle (not shown), what is the area of the triangle?(1)Point Q lies on the x-axis 6 units from point P.(2)Point R is 5 units away from the x-axisa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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