Question

100 POINT AND BRAINLIEST to correct answer answer UA AQ IE PI EP and DC
Use the Pythagorean Theorem to calculate the missing lengths, as indicated in each of the following items. Enter numerical answers, rounded to the nearest tenth of a unit, in the space provided.

1. Parallelogram QUAD is defined by coordinates (-2,-4) (6,-4) (11,2) and (3,2) respectively. Use the Pythagorean Theorem to find the length of side
UA= ____units.
2. Parallelogram is defined by the coordinates (-2,-4) (6,-4) (11,2) and (3,2) respectively. Use the Pythagorean Theorem to find the length of the parallelogram’s diagonal AQ=_____ units
Triangle PIE is defined by the coordinates(-2,-4) (6,-1/2) and (0,4) , respectively. the Pythagorean Theorem to find the lengths of the sides of the triangle.

2 IE___ units

3 PI___ units

4 EP___units
A circle with center D (0,-6) passes through the point C(5,-1). Use the Pythagorean Theorem to find the length of the circle’s radius, DC____ units.

Answer 1

1. UA 78 units 2. AQ 14.3 units 3.IE 7.5 units 4. PI 8.7 units 5.EP 8.2 units 6. d=11.0 units

Step-by-step explanation:

1. Here apply the formula for distance between two points in a segment as;

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

where x,y are coordinates values.

For UA where U(6,-4) and A(11,2) then the distance UA is calculated as;

$d=\sqrt{(11-6)^2+(2--4)^2} \\\\d=\sqrt{5^2+6^2} =\sqrt{25+36} =\sqrt{61} =7.8units$

2.

Finding AQ where A(11,2) and Q(-2,-4), then apply the same formula for distance as;

$d=\sqrt{(-2-11)^2+(-4-2)^2} \\\\\\d=\sqrt{-13^2+-6^2} \\\\d=\sqrt{169+36} =\sqrt{205} =14.3$

3.

Given the triangle with vertices , the length of the sides can be found by applying the distance formula as;

IE where I(6, -1/2) ,E(0,4) then,

$d=\sqrt{0-6)^2+(4--1/2)^2}\\ \\d=\sqrt{-6^2+4.5^2} \\\\d=\sqrt{36+20.25} =\sqrt{56.25} =7.5units$

PI where P(-2,-4) and I(6,-1/2) then,

$d=\sqrt{(6--2)^2+(-1/2--4)^2} \\\\\\d=\sqrt{8^2+3.5^2} =\sqrt{64+12.25} =\sqrt{76.25} =8.7units$

4.

EP where E(0,4) and P(-2,-4)

$d=\sqrt{(-2-0)^2+(-4-4)^2} \\\\\\d=\sqrt{-2^2+-8^2} =\sqrt{4+64} =\sqrt{68} =8.2units$

5.

The circle has a center at D(0,-6) and passes through point C(5,-1).To get the radius of the circle, you find the distance DC

Radius DC , where D(0,-6) ,C(5,-1)

$d=\sqrt{(-1-0)^2+(5--6)^2} \\\\d=\sqrt{-1^2+11^2} =\sqrt{1+121} =\sqrt{122} =11.0$

Learn More

Finding length of a segment given coordinates of end-point:https://brainly.com/question/285950

Keywords : Pythagorean ,lengths, parallelogram,coordinates,diagonal,triangle

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Answer 2

Answer:

1. UA 78 units

2. AQ 14.3 units

3.IE 7.5 units

4. PI 8.7 units

5.EP 8.2 units

6. d=11.0 units

Step-by-step explanation:

I hope this helps! :)