Question

Please help. I don't understand>

Answer 1

$\large\underline{\sf{Solution-}}$

Given a triangle RST such that,

• Coordinates of R is (2, 3)

• Coordinates of S is (6, 7)

• Coordinates of T is (4, 8)

We know,

Area of triangle is given by

$\boxed{\tt{ \sf \ Area =\dfrac{1}{2} \bigg | x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\bigg |}}$

So, here

• x₁ = 2

• x₂ = 6

• x₃ = 4

• y₁ = 3

• y₂ = 7

• y₃ = 8

So, on substituting the values, we get

$\rm :\longmapsto\:\sf \ Area =\dfrac{1}{2} \bigg |2(7 - 8) + 6(8 - 3) + 4(3 - 7)\bigg |$

$\rm :\longmapsto\:\sf \ Area =\dfrac{1}{2} \bigg |2( - 1) + 6(5) + 4( - 4)\bigg |$

$\rm :\longmapsto\:\sf \ Area =\dfrac{1}{2} \bigg | - 2 + 30 - 16\bigg |$

$\rm :\longmapsto\:\sf \ Area =\dfrac{1}{2} \bigg | 30 - 18\bigg |$

$\rm :\longmapsto\:\sf \ Area =\dfrac{1}{2} \bigg | 12\bigg |$

$\rm :\longmapsto\:\sf \ Area =6 \: square \: units$

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Learn More:

1. Section formula

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the point which divides PQ internally in the ratio m₁ : m₂. Then, the coordinates of R will be:

$\sf\implies \boxed{\tt{ R = \bigg(\dfrac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}}, \dfrac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\bigg)}}$

2. Mid-point formula

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the mid-point of PQ. Then, the coordinates of R will be:

$\sf\implies \boxed{\tt{ R = \bigg(\dfrac{x_{1}+x_{2}}{2}, \dfrac{y_{1}+y_{2}}{2}\bigg)}}$

3. Centroid of a triangle

Centroid of a triangle is the point where the medians of the triangle meet.

Let A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) be the vertices of a triangle. Let R(x, y) be the centroid of the triangle. Then, the coordinates of R will be:

$\sf\implies \boxed{\tt{ R = \bigg(\dfrac{x_{1}+x_{2}+x_{3}}{3}, \dfrac{y_{1}+y_{2}+y_{3}}{3}\bigg)}}$