First slide

Equation of line in Straight lines

Question

$The reflection of the orthocentre of the triangle formed by the points (2, 3), (2, 4) and$ $(5, 4) in x -axis is.$

Moderate

A

$(2, 4)$
B

$(- 2, - 4)$
C

$(4, 2)$
D

$(2, - 4)$

Solution

$The given points are A (2, 3), B (2, 4), C (5, 4)$
$Since the x -coordinates of two points A (2, 3), B (2, 4) are same, the line joining A, B is verticale line$
$Since y -coordinates of two points B (2, 4), C (5, 4) are same. the line joining B, C is$
$horizontal line, so that the triangle A B C is right angled triangle with vertex at right angle is B (2, 4)$
In right angled triangle, the ortho centre is vertex at right angle.
Hence, the ortho centre is $(2, 4)$ .
The reflection of a point $(x, y)$ in $x -$ axis is $(x, - y)$
Therefore, the reflection of $(2, 4)$ in $x -$ axis is $(2, - 4)$

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