Question

plzz ...... someone answerer this question ​

Answer 1

Answer:

c) 5/2 units

Step by step method provided in the images

Plz mark this answer as the Brainliest if it helps:-)

Answer 2

Question:

If A ( - 1, 2 ), B ( 0, 0 ), C ( 2, 1 ) are the vertices of a triangle ABC, then the length of median drawn through the vertex A is -

a) 5 units

b) 10 units

c) $\sf\dfrac{5}{2}\:units$

d) $\sf\dfrac{3}{2}\:units$

Answer:

The length of median drawn from point A is $\sf\:\dfrac{5}{2}\:units}$.

Option c) $\sf\dfrac{5}{2}\:units$

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

We have given that,

$\bullet\sf\:A\:\equiv\:(\:-\:1\:,\:2\:)\:\equiv\:(\:x_1\:,\:y_1\:)\\\\\\\bullet\sf\:B\:\equiv\:(\:0\:,\:0\:)\:\equiv\:(\:x_2\:,\:y_2\:)\\\\\\\bullet\sf\:C\:\equiv\:(\:2\:,\:1\:)$

In figure, seg AD is the median from the point A.

Point D is the midpoint of seg BC.

$\bullet\sf\:D\:\equiv\:(\:x\:,\:y\:)$

Now, we know that,

$\pink{\sf\:x\:=\:\dfrac{x_2\:+\:x_3}{2}\:,\:y\:=\:\dfrac{y_2\:+\:y_3}{2}}\sf\:\:\:-\:-\:[\:Midpoint\:Formula\:]\\\\\\\implies\sf\:x\:=\:\dfrac{0\:+\:2}{2}\:\:,\:\:y\:=\:\dfrac{0\:+\:1}{2}\\\\\\\implies\sf\:x\:=\:\dfrac{2}{2}\:\:,\:\:y\:=\:\dfrac{1}{2}\\\\\\\implies\boxed{\red{\sf\:x\:=\:1\:,\:y\:=\:\dfrac{1}{2}}}$

Now, we have to find the length of segment AD.

$\pink{\sf\:d\:(\:A\:,\:D\:)\:=\:\sqrt{(\:x\:-\:x_1\:)^2\:+\:(\:y\:-\:y_1\:)^2}}\sf\:\:\:-\:-\:[\:Distance\:formula\:]\\\\\\\implies\sf\:d\:(\:A\:,\:D\:)\:=\:\sqrt{[\:1\:-\:(\:-\:1\:)\:]^2\:+\:\left(\:\dfrac{1}{2}\:-\:2\:\right)^2}\\\\\\\implies\sf\:d\:(\:A\:,\:D\:)\:=\:\sqrt{\:(\:1\:+\:1\:)^2\:+\:\left(\:\dfrac{1\:-\:4}{2}\:\right)^2}\\\\\\\implies\sf\:d\:(\:A\:,\:D\:)\:=\:\sqrt{\:(\:2\:)^2\:+\:\left(\:\dfrac{-\:3\:}{2}\:\right)^2}\\\\\\\implies\sf\:d\:(\:A\:,\:D\:)\:=\:\sqrt{4\:+\:\dfrac{9}{4}}\\\\\\\implies\sf\:d\:(\:A\:,\:D\:)\:=\:\sqrt{\dfrac{16\:+\:9}{4}}\\\\\\\implies\sf\:d\:(\:A\:,\:D\:)\:=\:\sqrt{\dfrac{25}{4}}\\\\\\\implies\boxed{\red{\sf\:d\:(\:A\:,\:D\:)\:=\:\dfrac{5}{2}}}\sf\:\:-\:-\:[\:Taking\:square\:roots\:]$

The length of median drawn from point A is $\sf\:\dfrac{5}{2}\:units}$.