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# The point that bisects the line depicted in the figure above is:

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
The point that bisects the line depicted in the figure above is:  [#permalink]

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11 Jun 2019, 01:49
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Difficulty:

55% (hard)

Question Stats:

58% (01:28) correct 42% (02:01) wrong based on 73 sessions

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The point that bisects the line depicted in the figure above is:

A. (1.25 ; 0.75)

B. (1.25 ; 2.25)

C. (1.25 ; 2)

D. (1.25 ; 1.25)

E. (1.5 ; 1.25)

Attachment:

image521.jpg [ 3.63 KiB | Viewed 853 times ]

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Re: The point that bisects the line depicted in the figure above is:  [#permalink]

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11 Jun 2019, 02:00
By property of similar triangles, we can visualize a smaller right angled triangle with in a larger right angled triangle with the depicted line as hypotenuse.

Hence, the opposite sides and adjacent sides of the smaller triangle will be half as much as the larger one.

With coordinates from Option "A", it is possible to visualize.

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The point that bisects the line depicted in the figure above is:  [#permalink]

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11 Jun 2019, 06:30
4
Bunuel wrote:

The point that bisects the line depicted in the figure above is:

A. (1.25 ; 0.75)

B. (1.25 ; 2.25)

C. (1.25 ; 2)

D. (1.25 ; 1.25)

E. (1.5 ; 1.25)

Attachment:
image521.jpg

The only point on the line segment that would bisect it is its mid point

--> Midpoint of 2 points (x1, y1) and (x2, y2) = ($$\frac{(x1 + x2)}{2}$$, $$\frac{(y1 + y2)}{2}$$)

--> Midpoint of (0, -1.5) and (2.5, 3) = ($$\frac{(0 + 2.5)}{2}$$, $$\frac{(-1.5 + 3)}{2}$$)
= (1.25, 0.75)

IMO Option A

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Posts: 3158
Re: The point that bisects the line depicted in the figure above is:  [#permalink]

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12 Jun 2019, 03:07
Solution

To Find:
• The point that bisects the line depicted in the figure

Approach & Working Out:
• The point that bisects the line depicted in the figure = the mid-point of the line = $$\frac{(0 + 2.5)}{2}, \frac{( -1.5 + 3)}{2} = (1.25, 0.75)$$

Hence, the correct answer is Option A
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Re: The point that bisects the line depicted in the figure above is:  [#permalink]

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14 Jun 2019, 09:31
Bunuel wrote:

The point that bisects the line depicted in the figure above is:

A. (1.25 ; 0.75)

B. (1.25 ; 2.25)

C. (1.25 ; 2)

D. (1.25 ; 1.25)

E. (1.5 ; 1.25)

Attachment:
image521.jpg

We use the midpoint formula: ((x_1 + x_2)/2 , (y_1 + y_2)/2). The point that bisects the line is (2.5 + 0)/2, (3 - 1.5)/2 = (1.25, 0.75).

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
Re: The point that bisects the line depicted in the figure above is:  [#permalink]

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04 Oct 2019, 01:46
Bunuel wrote:

The point that bisects the line depicted in the figure above is:

A. (1.25 ; 0.75)

B. (1.25 ; 2.25)

C. (1.25 ; 2)

D. (1.25 ; 1.25)

E. (1.5 ; 1.25)

Attachment:
image521.jpg

Official Explanation

The midpoint between any two points is found by averaging the two points' x-coordinates and their y-coordinates. (This can be proved from the Pythagorean Theorem, which also gives us the distance between two points in the coordinate plane.) The average of 2.5 and 0 is 1.25, so that is the x-coordinate of the midpoint. The average of 3 and -1.5 is 0.75. The answer is (A).

Another approach here would be two find the equation of the line in the form y = mx + b. You can determine the slope m from the rise over run between the two points. The y-intercept b is -1.5. Then you could find the point on the line that is halfway along the run, at an x-value of 1.25, and you would find that at that x-value, y = 0.75.

Again, the correct answer is (A).
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Math Expert
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Posts: 59587
Re: The point that bisects the line depicted in the figure above is:  [#permalink]

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04 Oct 2019, 01:47
Bunuel wrote:

The point that bisects the line depicted in the figure above is:

A. (1.25 ; 0.75)

B. (1.25 ; 2.25)

C. (1.25 ; 2)

D. (1.25 ; 1.25)

E. (1.5 ; 1.25)

Attachment:
image521.jpg

Video Explanation

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Re: The point that bisects the line depicted in the figure above is:   [#permalink] 04 Oct 2019, 01:47
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# The point that bisects the line depicted in the figure above is:

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