First slide

Equation of line in Straight lines

Question

$ABCD$ is a square . $A \equiv (1, 2), B (3, - 4) .$ If line CD passes through $(3, 8)$ , then the midpoint of CD is

Moderate

A

$(2, 6)$
B

$(6, 2)$
C

$(2, 5)$
D

$(28 / 5, 1 / 5)$

Solution

$m_{AB} = \frac{- 4 - 2}{3 - 1} = - 3$
Thus, the equation of CD is $y - 8$
$= 3 (x - 3), i . e ., y + 3 x = 17 .$
The equation of the right bisector of AB is
$y + 1 = \frac{1}{3} (x - 2)$
or $3 y = x - 5$
Solving it with line CD, we get $x = 28 / 5, y = 1 / 5 .$ Thus the midpoint of CD is $(28 / 5, 1 / 5)$

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