MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

The Orthocentre

If the point ...

Question

If the point $(0, β)$ lies on or inside the triangle formed by the lines $y = 0$ , $x + y = 8$ and $3 x - 4 y + 12 = 0$ , then $β$ cannot be equal to

A

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

12

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
B $4$
C $8$
D $12$
For the point $(0, β)$ to be on or inside the triangle
$(i) β \geq 0$
$(i i) β - 8 \leq 0 \Rightarrow β \leq 8$
$(i i i) - 4 β + 12 \geq 0 \Rightarrow β \leq 3$
$\Rightarrow 0 \leq β \leq 3$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Let the lines

y - k_{1} x - β = 0

y - k_{2} x - β = 0, (k_{1} \neq k_{2}), k_{1}, k_{2} \in R

P

x - p_{1} y - α = 0

x - p_{2} y - α = 0, (p_{1} \neq p_{2}), p_{1}, p_{2} \in R

Q

. If the points

P

Q

always lies on or inside the triangle formed by the lines

2 x - 3 y - 6 = 0, 3 x - y + 3 = 0

3 x + 4 y - 12 = 0

(1, β)

lies on or inside the triangle formed by the lines

y = x

x + y = 8

Q. The condition to be imposed on

β

(0, β)

lies on or inside the triangle having sides y + 3x + 2 = 0, 3y – 2x – 5 = 0 and 4y + x – 14 = 0 is

(1, β)

lies on or inside the triangle formed by the lines y = x, x - axis and x + y =8

Q. The set of values of

β

so that the point

(0, β)

lies inside or on the triangle having the sides

3 x + y + 2 = 0, 2 x - 3 y + 5 = 0

x + 4 y - 14 = 0

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Altitude of a triangle

MATHEMATICS

Watch in App

explore_more_icon

Explore more

The Orthocentre

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon