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Point Q(b,−1) is the midpoint of segment EF. Co-ordinates of point E are (−4, a) and point F are (2,0). What is the value of a and b?
Correct answer is '-2, -1'. Can you explain this answer?
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Most Upvoted Answer
Point Q(b,−1) is the midpoint of segment EF. Co-ordinates of point E ...
Given,
Point Q(b,−1) is the midpoint of segment with endpoints E(−4, a) and F(2, 0).
As we know,
The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by,
On comparing, we get
b = −1, a = −2
Hence, the correct answer is a = -2, b = -1.
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Community Answer
Point Q(b,−1) is the midpoint of segment EF. Co-ordinates of point E ...
Understanding Midpoints
To find the coordinates of point Q, which is the midpoint of segment EF, we use the midpoint formula. The coordinates of the midpoint M between two points E(x1, y1) and F(x2, y2) are given by:
M = ((x1 + x2)/2, (y1 + y2)/2).
Coordinates of Points E and F
- E has coordinates (-4, a)
- F has coordinates (2, 0)
Applying the Midpoint Formula
Using the coordinates of points E and F:
- For the x-coordinate of Q:
- x-coordinate of Q = (x1 + x2)/2
- x-coordinate of Q = (-4 + 2)/2 = (-2)/2 = -1
- For the y-coordinate of Q:
- y-coordinate of Q = (y1 + y2)/2
- y-coordinate of Q = (a + 0)/2 = a/2
Setting Up the Equations
Point Q is given as (b, -1), so we can set up the following equations:
1. b = -1
2. a/2 = -1
Solving for a and b
From the first equation, we directly find:
- b = -1
From the second equation:
- a/2 = -1
- a = -1 * 2
- a = -2
Final Values
Thus, the values of a and b are:
- a = -2
- b = -1
This confirms that point Q(b, -1) is indeed the midpoint of segment EF, with the coordinates of E being (-4, -2) and F being (2, 0).
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Point Q(b,−1) is the midpoint of segment EF. Co-ordinates of point E are (−4, a) and point F are (2,0). What is the value of a and b?Correct answer is '-2, -1'. Can you explain this answer?
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