the line 2x+3y=12 meets the x axis at A and y axis at B The line through (5,5) perpendicular to - Maths - Straight Lines

Question

the line 2x+3y=12 meets the x axis at A and y axis at B The line
through (5,5) perpendicular to AB meets the x axis and AB at C and
If O is the origin of coordinates ,find the area of OCEB

Himanshu · Accepted Answer

Co-ordinates of A will be (6, 0) and co-ordinates of B will be (0, 4)

Slope of AB is - 2/3.

Slope of the line perpendicular to AB = (3/2)

Equation of line passing through (5, 5) and slope - (3/2) will be:

$y - 5 = \frac{3}{2} (x - 5) \Rightarrow 2 y - 3 x = - 5$

Co-ordinates of point C will be (5/3, 0)

Intersection points of 2x + 3y = 12 and 2y - 3x = - 5 will be (3, 2) and is the point E.

Area of OCEB will be area of triangle EBO and area of triangle EOC

$Δ O E B = \frac{1}{2} O B \times 3 = 6 Δ O E C = \frac{1}{2} O C \times 2 = \frac{1}{2} \times \frac{5}{3} \times 2 = \frac{5}{3} O C E B = \frac{23}{3}$

Area of OCEB will be area of triangle EBO and area of triangle EOC $Δ O E B = \frac{1}{2} O B \times 3 = 6 Δ O E C = \frac{1}{2} O C \times 2 = \frac{1}{2} \times \frac{5}{3} \times 2 = \frac{5}{3} O C E B = \frac{23}{3}$

the line 2x+3y=12 meets the x axis at A and y axis at B.The line through (5,5) perpendicular to AB meets the x axis and AB at C and.If O is the origin of coordinates ,find the area of OCEB