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# In the figure above, what are the coordinates of the midpoint of PQ ?

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
In the figure above, what are the coordinates of the midpoint of PQ ?  [#permalink]

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19 Feb 2018, 22:58
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5% (low)

Question Stats:

85% (00:33) correct 15% (00:58) wrong based on 58 sessions

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In the figure above, what are the coordinates of the midpoint of PQ ?

(A) (x, y)

(B) (x, 0)

(C) (0, 0)

(D) (0, y)

(E) (-x, -y)

Attachment:

2018-02-20_0956.png [ 6 KiB | Viewed 889 times ]

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In the figure above, what are the coordinates of the midpoint of PQ ?  [#permalink]

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20 Feb 2018, 03:59
Bunuel wrote:

In the figure above, what are the coordinates of the midpoint of PQ ?

(A) (x, y)

(B) (x, 0)

(C) (0, 0)

(D) (0, y)

(E) (-x, -y)

Attachment:
2018-02-20_0956.png

Mid point formula = (x1 + x2/2 , y1+y2/2 ) = x+x /2 , y + (-y) /2 = 2x/2 , 0 /2 = x, 0

(B) imo
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Joined: 22 May 2016
Posts: 3077
In the figure above, what are the coordinates of the midpoint of PQ ?  [#permalink]

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20 Feb 2018, 18:17
1
Bunuel wrote:

In the figure above, what are the coordinates of the midpoint of PQ ?

(A) (x, y)

(B) (x, 0)

(C) (0, 0)

(D) (0, y)

(E) (-x, -y)

Attachment:
2018-02-20_0956.png

For a vertical line, x always has the same value, no matter what value y takes. The equation for such a line is $$x = a$$, and $$a$$ is the x-intercept (what x equals when y = 0).

Here, the equation for segment PQ is x = x. That is, x takes a's place on RHS. (RHS "x" could have been k, 2, Z, @, 15, etc.)

The midpoint of PQ lies on the line x = x. Its x-coordinate is $$x$$.

Eliminate answers C, D, and E

The y-coordinate for the midpoint is 0. Use
Midpoint formula:
$$\frac{y_1+y_2}{2}=\frac{-y+y}{2}=\frac{0}{2}=0$$
OR
Use the rule about reflection over the x-axis.

Rule: If a point is reflected over the x-axis, then
$$(x,y) -> (x, -y)$$

Those are the coordinates of these two points. They are reflected over the x-axis. The distance of y from the x-axis equals the distance of -y from the x-axis. The halfway point is the x-axis, whose equation is y = 0.

Midpoint coordinates are (x,0)

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Re: In the figure above, what are the coordinates of the midpoint of PQ ?  [#permalink]

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22 Feb 2018, 09:16
Bunuel wrote:

In the figure above, what are the coordinates of the midpoint of PQ ?

(A) (x, y)

(B) (x, 0)

(C) (0, 0)

(D) (0, y)

(E) (-x, -y)

Attachment:
2018-02-20_0956.png

Using the midpoint formula ((x1 + x2)/2 , (y1 + y2)/2) we have:

(x + x)/2, (y + (-y))/2 = (x, 0)

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Re: In the figure above, what are the coordinates of the midpoint of PQ ?   [#permalink] 22 Feb 2018, 09:16
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