Question:
A and B are two points on the x-axis and y-axis respectively. P (2, – 3) is the mid point of AB. Find the:
(i) the co-ordinates of A and B.
(ii) the slope of the line AB.
(iii) the equation of the line AB.
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Answers & Comments
1) Let the coordinates be A(x, 0) and B(0, y)
Mid-point of A and B is given by ((x + 0)/2, (y + 0)/2) = (x/2, y/2)
Rightarrow (2, - 3) = (x/2, y/2)
Rightarrow x/2 =2:
and
y/2 = - 3
=> x = 4 and y = 6
A(4, 0) and B(0, - 6)
2) Slope of line AB, m = (y_{2} - y_{1})/(x_{2} - x_{1}) = (- 6 + 0)/(0 - 4) = 3/2
3) Equation of line AB, using A(4,0)
y-0 3/2(x −4)
⇒ 3x - 2y = 12
Hope it helps ya..
Verified answer
Given :-
P(2, -3)
Assume that,
then,
[tex]2 = \frac{x + 0}{2} \\ = > x = 2 \times 2 \\ = > x = 4[/tex]
and
[tex] - 3 = \frac{0 + y}{2} \\ = > - 3 \times 2 = y \\ = > y = - 6[/tex]
So, [tex]x = 4[/tex] and [tex]y = - 6[/tex]
Now, as per sub-questions,
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(i) Coordinates are :-
( I directly substituted the values )
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(ii) Slope of AB =
[tex] \frac{y_2 - y_1}{x_2 - x_1} \\ [/tex]
[tex] = > \frac{ - 6 - 0}{0 - 4} \\ = > \frac{ - 6}{ - 4} \\ = > \frac{6}{4} \\ \\ = > \frac{3}{2}[/tex]
(iii) Check attached image for explanation.
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