Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

A(6, 1), B(8, 2) and C(9, 4) are the vertices of a parallelogr

Question

$A (6, 1), B (8, 2)$ and $C (9, 4)$ are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of $Δ A D E$ .

Views: 753 students

Found 6 tutors discussing this question

James Discussed

A (6, 1), B (8, 2)

and

C (9, 4)

are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of

Δ A D E

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

A (6, 1), B (8, 2)

and

C (9, 4)

are the three vertices of a parallelogram ABCD.

E is the midpoint of DC.

Join AE, AC and BD which intersects at O, where Q is midpoint of AC.

Midpoint formula:

(x, y) = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

Find coordinates of midpoints D and E:

\frac{x + 8}{2} = \frac{15}{2} \Rightarrow x + 8 = 15

x = 15 - 8 = 7

and

\frac{y + 2}{2} = \frac{5}{2} \Rightarrow y + 2 = 5

y = 5 - 2 = 3

Coordinate of D are

(7, 3)

And

= (\frac{7 + 9}{2}, \frac{3 + 4}{2})

= (8, \frac{7}{2})

Coordinate of E are

(7, 3)

Now, We know that:

Area of

Δ A BC = \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]

Area of

Δ A D C

= \frac{1}{2} [6 (3 - \frac{7}{2}) + 7 (\frac{7}{2} - 1) + 8 (1 - 3)]

= \frac{1}{2} [6 \times (\frac{- 1}{2}) + 7 \times \frac{5}{2} + 8 (- 2)]

= \frac{5}{2} [- 3 + \frac{35}{2} - 16]

= \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}

sq. units.

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	$A (6, 1), B (8, 2)$ and $C (9, 4)$ are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of $Δ A D E$ .
Answer Type	Text solution:1
Upvotes	150

A(6,1),B(8,2) and C(9,4) are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ΔADE.

Text solutionVerified

Practice questions from similar books

$A (6, 1), B (8, 2)$ and $C (9, 4)$ are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of $Δ A D E$ .