Ask question

# The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle. (-4,3), (0,5), and (3,-4) # The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle. (-4,3), (0,5), and (3,-4)

Question
Right triangles and trigonometry asked 2021-01-15
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-4,3), (0,5), and (3,-4)

## Answers (1) 2021-01-16
We know that the square of distance between two points $$(x_1,y_1) and (x_2,y_2) is (x_2-x_1)^2+(_y2-y_1)^2$$ and the converse of pythagorus theorem , we have if sum of square of any two side is equal to square of third side of triangle, then it is right angled triangle.
Using distance formula and converse of pythagorus theorem , we find that ABC is right angled triangle right angled at A
A(-4,3), B(0,5), C(3,-4)
$$c^2=|AB|^2=(0+4)^2+(5-3)^2=16+4=20$$
$$a^2=|BC|^2=(3-0)^2+(-4-5)^2=9+81=90$$
$$b^2=|CA|^2=(3+4)^2+(-4-3)^2=49+49=98$$
$$a^2!=b^2+c^2$$
$$98 != 90+20$$

### Relevant Questions asked 2021-03-02
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-4,3), (0,5), and (3,-4) asked 2021-02-03
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-3,1), (2,-1), and (6,9) asked 2020-12-29
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-3,1), (2,-1), and (6,9) asked 2021-02-02
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-3,1), (2,-1), and (6,9) asked 2021-05-18
The student engineer of a campus radio station wishes to verify the effectivencess of the lightning rod on the antenna mast. The unknown resistance $$\displaystyle{R}_{{x}}$$ is between points C and E. Point E is a "true ground", but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth's surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance $$\displaystyle{R}_{{y}}$$. The procedure for finding the unknown resistance $$\displaystyle{R}_{{x}}$$ is as follows. Measure resistance $$\displaystyle{R}_{{1}}$$ between points A and B. Then connect A and B with a heavy conducting wire and measure resistance $$\displaystyle{R}_{{2}}$$ between points A and C.Derive a formula for $$\displaystyle{R}_{{x}}$$ in terms of the observable resistances $$\displaystyle{R}_{{1}}$$ and $$\displaystyle{R}_{{2}}$$. A satisfactory ground resistance would be $$\displaystyle{R}_{{x}}{<}{2.0}$$ Ohms. Is the grounding of the station adequate if measurments give $$\displaystyle{R}_{{1}}={13}{O}{h}{m}{s}$$ and R_2=6.0 Ohms? asked 2021-04-11
The equation F=−vex(dm/dt) for the thrust on a rocket, can also be applied to an airplane propeller. In fact, there are two contributions to the thrust: one positive and one negative. The positive contribution comes from air pushed backward, away from the propeller (so dm/dt<0), at a speed vex relative to the propeller. The negative contribution comes from this same quantity of air flowing into the front of the propeller (so dm/dt>0) at speed v, equal to the speed of the airplane through the air.
For a Cessna 182 (a single-engine airplane) flying at 130 km/h, 150 kg of air flows through the propeller each second and the propeller develops a net thrust of 1300 N. Determine the speed increase (in km/h) that the propeller imparts to the air. asked 2021-03-22
A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant but starts at .100 at P and increases linerly with distance past P, reaching a value of .600 at 12.5 m past point P. (a) Use the work energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid iff the friciton coefficient didn't increase, but instead had the constant value of .1? asked 2021-05-02
Suppose electrons enter the uniform electric field midwaybetween two plates, moving at an upward 45 degree angle as shown.What maximum speed can the electrons have if they are to avoidstriking the upper plate. Ignore fringing of the field. Upper plate is negatively charged bottom plate is positivelycharged length of plate is 6cm and distance from top of top plateto bottom of bottom plate is 1cm.
$$\displaystyle{E}={5.0}\times{10}^{{3}}\frac{{N}}{{C}}$$ asked 2021-02-26
The top string of a guitar has a fundamental frequency of 33O Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck to the bridge. A fret is provided for limiting vibration to just the lower two thirds of the string, If the string is pressed down at this fret and plucked, what is the new fundamental frequency? The guitarist can play a "natural harmonic" by gently touching the string at the location of this fret and plucking the string at about one sixth of the way along its length from the bridge. What frequency will be heard then? asked 2021-02-10
Two light sources of identical strength are placed 8 m apart. An object is to be placed at a point P on a line ? parallel to the line joining the light sources and at a distance d meters from it (see the figure). We want to locate P on ? so that the intensity of illumination is minimized. We need to use the fact that the intensity of illumination for a single source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. ...