Question

The points A(4,-2), B(7,2),C(0,9),D(-3,5)form a parallelogram. Find the length of the altitude of the parallelogram on the base AB.

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Answer 1

The answer is 9.8 units.

Please refer the above photograph for the used process.

Hope this will be helping you.


KEY POINTS TO REMEMBER :-


☸️ DISTANCE FORMULA :-

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$


☸️ AREA OF TRIANGLE :-

$\frac{1}{2} \times (x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))$

☸️ AREA OF PARALLELOGRAM :-

$base \times altitude$

Thanks!

Answer 2

$\huge \bf \green{Hey \: there !! }$


$\large \boxed{ \underline{ \bf Coordinate \: Geometry .}}$


▶ Question :-

→ The points A(4,-2), B(7,2),C(0,9),D(-3,5)form a parallelogram. Find the length of the altitude of the parallelogram on the base AB.


▶ Answer :-

$\large\pink{ \mid\underline{ \overline{ \bf See \: the \: attachment.}} \mid}$


▶ Identity or formula used :-

→ ar( ||gm ABCD ) = 2 × ( ∆ABC ) .

$\implies ar( \triangle ABC) = \frac{1}{2} \mid x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \mid.$


→ Distance formula :-

$\implies distance = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} } .$


→ ar( ||gm ABCD ) = Base × Height .



$\bf Altitude = \large{ \boxed{ \boxed{ \orange{ \bf \: 9.8 \: units.}}}}$



✔✔ Hence, it is solved ✅✅.



THANKS


#BeBrainly.