1) gradient of line = Δ y ÷ Δ x
= (5 -2) ÷ (3 - (-6))
= ¹/₃

using the point-slope form (y-y₁) = m(x-x₁)
using (3,5)
(y - 5) = ¹/₃ (x -3)
   y - 5 = ¹/₃x - 1
⇒ <span> y = ¹/₃ x + 4 [OPTION D]

</span>2)    y = 2x + 5 .... (1)
<span>    </span>y = ¹/₂ x + 6 .... (2)

by substituting y in (1) for y in (2)

2x + 5 = ¹/₂ x + 6
   ³/₂ x = 1
x = ²/₃

by substituting found x (2)

    y = ¹/₂ (²/₃) + 6
y = ¹⁹/₃

∴ common point is (²/₃ , ¹⁹/₃) thus answer is FALSE [OPTION B]

3) Yes [OPTION A]
This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.

4) No [OPTION B]
Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other. Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.

6 0

3 years ago

In triangle ABC, angle bisectors line AD, line BE, and line CF meet at I. If DI = 3, BD = 4, and BI = 5, then compute the area o

Nikitich [7]

The area of triangle ABC is the amount of space on the triangle

The area of the triangle is 54.84 square units

<h3>How to determine the area of triangle ABC</h3>

Start by drawing the triangle (see attachment)

Next, calculate the measure of angle B using the following tangent ratio

$\tan(B/2) = \frac 34$