Find the coordinates of the midpoint of the segment whose endpoints are H(2, 1) and K(10, 7)

Answers

Answer 1

Answer: $\bf \textit{middle point of 2 points }\n \quad \n \begin{array}{lllll} &x_1&y_1&x_2&y_2\n % (a,b) H&({{ 2}}\quad ,&{{ 1}})\quad % (c,d) K&({{ 10}}\quad ,&{{ 7}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

you tell us

Answer 2

Answer:

Answer:

Find the coordinates of the midpoint of the segment whose endpoints are H(2, 1) and K(10, 7).

Step-by-step explanation:

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The domain of a function is given by {-4,2,8}. If the function is defined by y= x +1 /3 ,then which of the following values is a member of the range?

Answers

Answer:

{-1, 1, 3}

Step-by-step explanation:

Given the function

y = (x + 1)/3

The domain are the input value x while the range are the output values given the input value x;

Given the domain {-4, 2, 8}

when x = -4;

y = (-4+1)/3

y = -3/3

y = -1

when x = 2;

y = (2+1)/3

y = 3/3

y = 1

when x = 8;

y = (8+1)/3

y = 9/3

y = 3

Hence the member of the range are {-1, 1, 3}

BD bisects ABC, m/ABC =8x, m/ABD=2x + 30. Find m/DBC.

Answers

Answer:

Step-by-step explanation:

To find the measure of angle DBC, we can use the angle bisector theorem, which states that in a triangle, if a line bisects one of the angles, it divides the opposite side into segments proportional to the other two sides. In this case, BD bisects angle ABC, so:m∠ABD / m∠DBC = AB / BCWe are given:

m∠ABC = 8x

m∠ABD = 2x + 30So, we have:(2x + 30) / m∠DBC = AB / BCNow, we need to express AB / BC in terms of x. To do that, we'll use the fact that angles in a triangle add up to 180 degrees:m∠ABC + m∠ABD + m∠DBC = 180Substitute the given angle measures:8x + (2x + 30) + m∠DBC = 180Combine like terms:10x + 30 + m∠DBC = 180Now, isolate m∠DBC:m∠DBC = 180 - 10x - 30

m∠DBC = 150 - 10xNow, we can substitute this expression for m∠DBC back into our proportion:(2x + 30) / (150 - 10x) = AB / BCNow, you can solve for m∠DBC:Cross-multiply:(2x + 30)(BC) = (150 - 10x)(AB)Now, you would need more information about the relationship between AB and BC or additional angle measures to solve for the exact value of m∠DBC. Without that additional information, you can't determine the specific angle measure.

Which of these triangle pairs can be mapped to each other using two reflections? Triangles X Y Z and P Y T are connected at point Y. Triangle X Y Z is reflected across X Y and then is reflected another time across Y Z to form triangle P Y T. Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected 3 times to form triangle A Y T. Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected across side X Y and then is shifted down to form triangle A Y T. Triangles X Y Z and A Z T are connected at point Z. Triangle X Y Z is reflected and then rotated to form triangle A Z T.

Answers

The correct option is (A). $\Delta XYZ$ and $\Delta PYT$ are connected at point Y. $\Delta XYZ$ is reflected across XY and then is reflected another time across YZ to form $\Delta PYT$ .

Given, $\Delta XYZ$ and $\Delta PYT$ are connected at point Y.

$\Delta XYZ$ is reflected about XY will shift the marked angle from left to right while the right side angle will remain at the same location and the triangle will remain upright to give $\Delta X'Y'Z'.$

Reflection about the YZ will give the marked angle and the right angle in the same location and the vertex X will then be changed to P.

Thus , $\Delta XYZ$ can be mapped to $\Delta PYT$ with two reflections.

In the second option, we have $\Delta XYZ$ is reflected 3 times which is more than 2 times as said in question. so this statement is false.

In next option $\Delta XYZ$ is reflected across side XY and then is shifted downwards to form $\Delta AYT$ .since here we have only one reflection, so this statement is also false.

4) In option 4 $\Delta XYZ$ is reflected and then rotated thus option 4 is also not a correct option.

Hence the correct statement is $\Delta XYZ$ and $\Delta PYT$ are connected at point Y. $\Delta XYZ$ is reflected across XY and then is reflected another time across YZ to form $\Delta PYT$ .

For more detail follow the link:

brainly.com/question/8668014

Answer:

The correct option is the first option;

Triangle XYZ and PYT are connected at point Y. Triangle XYZ is reflected across XY and then is reflected another time across YZ to form triangle PYT

Step-by-step explanation:

To answer the question we look at each option as follows;

1) The parameters given are triangle XYZ and PYT are connected at point Y

Triangle XY is reflected about XY will shift the marked angle from left to right while the right angle will remain at the same location and the triangle will remain upright to give triangle X'Y'Z'

Reflection about the YZ will give; the marked angle and the right angle in the same location and the vertex X will then be changed to P

Therefore, triangle XYZ can be mapped to triangle PYT with two reflections

2) In the second option, we have triangle XYZ is reflected 3 times which is more than 2 times as in the question, therefore, option two is less suited as an answer to the question

3) Triangle XYZ is reflected across side XY and then is shifted down to form triangle AYT

Therefore, since we have only one reflection, option 3 is also not appropriate as an answer

4) In option 4 triangle XYZ is reflected and then rotated therefore option 4 is also not a correct option.

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