The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side.Find the lengths of the medians of the trangle with vertices at A=(0,0), B=(6,0), and C= (4,4).

yasusar0
2022-07-27
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Eve Good

Answered 2022-07-28
Author has **18** answers

A=(0,0), B=(6,0), and C= (4,4).

M is a midpoint of |AB|

$M(x,y)=(\frac{0+6}{2},\frac{0+0}{2})=(3,0)$

according to your figure $|MC|=\sqrt{(4-3{)}^{2}+(4-0{)}^{2}}=\sqrt{1+16}=\sqrt{17}$

M is a midpoint of |AB|

$M(x,y)=(\frac{0+6}{2},\frac{0+0}{2})=(3,0)$

according to your figure $|MC|=\sqrt{(4-3{)}^{2}+(4-0{)}^{2}}=\sqrt{1+16}=\sqrt{17}$

asked 2022-07-13

Convert from radians to degrees:

$-\frac{7\pi}{2}$

$-\frac{7\pi}{2}$

asked 2022-05-10

If K is the midpoint of AH, $P\in AB$, $Q\in AC$ and $K\in PQ$ such that $OK\perp PQ$ , then $OP=OQ$

asked 2022-08-04

Choose 3 inequalities that form a system whose graph is the shaded region shown above.

$A.y\le -2\phantom{\rule{0ex}{0ex}}B.y\ge -2\phantom{\rule{0ex}{0ex}}C.7x-4y\ge -13\phantom{\rule{0ex}{0ex}}D.7x+2y\ge 17\phantom{\rule{0ex}{0ex}}E.7x-4y\le -13\phantom{\rule{0ex}{0ex}}F.7x+2y\le 17\phantom{\rule{0ex}{0ex}}G.x\ge -2\phantom{\rule{0ex}{0ex}}H.y\le 2$

$A.y\le -2\phantom{\rule{0ex}{0ex}}B.y\ge -2\phantom{\rule{0ex}{0ex}}C.7x-4y\ge -13\phantom{\rule{0ex}{0ex}}D.7x+2y\ge 17\phantom{\rule{0ex}{0ex}}E.7x-4y\le -13\phantom{\rule{0ex}{0ex}}F.7x+2y\le 17\phantom{\rule{0ex}{0ex}}G.x\ge -2\phantom{\rule{0ex}{0ex}}H.y\le 2$

asked 2022-05-29

I want to show that $2{p}_{n-2}\ge {p}_{n}-1$...

Bertand's postulate shows us that $4{p}_{n-2}\ge {p}_{n}$ but can we improve on this?

any ideas?

Bertand's postulate shows us that $4{p}_{n-2}\ge {p}_{n}$ but can we improve on this?

any ideas?

asked 2022-05-07

How can I prove the following two questions:

Prove using Peano's Postulates for the Natural Numbers that if a and b are two natural numbers such that a + b = a, then b must be 0?

Prove using Peano's Postulates for the Natural Numbers that if a and b are natural numbers then: a + b = 0 if and only if a = 0 and b = 0?

I understand the basic postulates, but not sure how to apply them to these specific questions. The questions seem so basic and obvious, but when it comes to applying the postulates I am lost.

Prove using Peano's Postulates for the Natural Numbers that if a and b are two natural numbers such that a + b = a, then b must be 0?

Prove using Peano's Postulates for the Natural Numbers that if a and b are natural numbers then: a + b = 0 if and only if a = 0 and b = 0?

I understand the basic postulates, but not sure how to apply them to these specific questions. The questions seem so basic and obvious, but when it comes to applying the postulates I am lost.

asked 2022-07-18

Theorem: If a is a real number, then $a\cdot 0=0$.

1. $a\cdot 0+0=a\cdot 0$ (additive identity postulate)

2. $a\cdot 0=a\cdot (0+0)$ (substitution principle)

3. $a\cdot (0+0)=a\cdot 0+a\cdot 0$ (distributive postulate)

4. $a\cdot 0+0=a\cdot 0+a\cdot 0$ I'm lost here, wanna say its the transitive

5. $0+a\cdot 0=a\cdot 0+a\cdot 0$ (commutative postulate of addition)

6. $0=a\cdot 0$ (cancellation property of addition)

7. $a\cdot 0=0$ (symmetric postulate)

So I'm not sure what to put down for the 4th step. The theorem and proof were given and I had to list the postulates for each step.

1. $a\cdot 0+0=a\cdot 0$ (additive identity postulate)

2. $a\cdot 0=a\cdot (0+0)$ (substitution principle)

3. $a\cdot (0+0)=a\cdot 0+a\cdot 0$ (distributive postulate)

4. $a\cdot 0+0=a\cdot 0+a\cdot 0$ I'm lost here, wanna say its the transitive

5. $0+a\cdot 0=a\cdot 0+a\cdot 0$ (commutative postulate of addition)

6. $0=a\cdot 0$ (cancellation property of addition)

7. $a\cdot 0=0$ (symmetric postulate)

So I'm not sure what to put down for the 4th step. The theorem and proof were given and I had to list the postulates for each step.

asked 2022-06-14

The way I view Euclid's postulates are as follows:

A line segment can be made between any two points on surface A.

A line segment can be continued in its direction infinitely on surface A.

Any line segment can form the diameter of a circle on surface A.

The result of an isometry upon a figure containing a right angle preserves the right angle as a right angle on surface A.

If a straight line falling on two straight lines make the interior angles on the same side less than 180 degrees in total, the two straight lines will eventually intersect on the side where the sum of the angles is less than l80 degrees.

The way I view the five postulates is simple. Each postulate defines some quality a surface has.

For instance, 2 seems to define whether a surface is infinite/looped or finite/bounded, 3 seems to force a surface to be circular (or a union of circular subsets), and 5 I believe change the constant curvature of a surface (wether it is 0 or nonzero).

I want to determine what "quality" 1 and 4 define in the context of the surface itself. 1 seems to imply discontinuity vs continuity, and I think 4 would imply non-constant curvature. However, I am unsure. Ultimately I would like to assign each of these a quality of a surface that they define such that all surfaces can be "categorized" under some combination of postulates, but that is irrelevant.

I am merely asking:

What two surfaces individually violate the first postulate and violate the fourth postulate?

A line segment can be made between any two points on surface A.

A line segment can be continued in its direction infinitely on surface A.

Any line segment can form the diameter of a circle on surface A.

The result of an isometry upon a figure containing a right angle preserves the right angle as a right angle on surface A.

If a straight line falling on two straight lines make the interior angles on the same side less than 180 degrees in total, the two straight lines will eventually intersect on the side where the sum of the angles is less than l80 degrees.

The way I view the five postulates is simple. Each postulate defines some quality a surface has.

For instance, 2 seems to define whether a surface is infinite/looped or finite/bounded, 3 seems to force a surface to be circular (or a union of circular subsets), and 5 I believe change the constant curvature of a surface (wether it is 0 or nonzero).

I want to determine what "quality" 1 and 4 define in the context of the surface itself. 1 seems to imply discontinuity vs continuity, and I think 4 would imply non-constant curvature. However, I am unsure. Ultimately I would like to assign each of these a quality of a surface that they define such that all surfaces can be "categorized" under some combination of postulates, but that is irrelevant.

I am merely asking:

What two surfaces individually violate the first postulate and violate the fourth postulate?