Find the length of line pq if pq is parallel to bc and pq is a midsegment of triangle abc

Your answer is roughly 4.92 units, or √24.25 .

To find the length of line PQ, we need the coordinates of P and Q, and then we can use Pythagoras's theorem to find the distance between them. Because we know that PQ is a midsegment of triangle ABC, and also that it's parallel to BC, the coordinates of P and Q must be the midpoints of the lines AB and AC in the triangle.

To find a midpoint of a line, you add up the x coordinates and then half the result, and then add up the y coordinates and half the result. This means the midpoint of line AB is ( (8+1)/2, (6+1)/2 )= (4.5, 3.5). We can then label this point Q.

The midpoint of line AC is therefore ( (8+10)/2, (6-3)/2) = (9, 1.5). We can label this point Q.

Now to find the length of PQ, we can use Pythagoras's theorem. First we need to find the difference between the x coordinates and y coordinates of P and Q to be the legs of the right-angled triangle. These will be (9 - 4.5) = 4.5 for the base, and (3.5 - 1.5) = 2 for the height.

Thus, the length of PQ is √(2² + 4.5²) = √(4 + 20.25) = √24.25 . This is roughly equal to 4.92.

I hope this helps! Let me know if you have any questions :)

the image point of (0,4) after a translation right 2 units and down 3 units is (2,1) .

Step-by-step explanation:

Here we have , to find  the image point of (0,4)  after a translation right 2 units and down 3 units. Let's find out:

Initially we have the point as  (0,4)  , Following transformations are done :

a translation right 2 units :

The point is (0,4) , let . Translation is 2 units right , means there is change in x coordinate by +2 , i.e.

⇒

⇒

⇒

a translation down 3 units:

The point is (2,4)  , let . Translation is 3 units down , means there is change in y coordinate by -3 , i.e.

⇒

⇒

⇒

Therefore , the image point of (0,4) after a translation right 2 units and down 3 units is (2,1) .