<u>Answer-</u>
<em>The coordinates of the orthocenter of △JKL is (-4, 8)</em>
<u>Solution-</u>
The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.
For a right angle triangle, the vertex at the right angle is the orthocentre of the triangle.
Here we are given the three vertices of the triangle are J(-4,-1), K(-4,8) and L(2,8)
If the triangle JKL satisfies Pythagoras Theorem, then triangle JKL will be a right angle triangle.
Applying distance formula we get,
![JK^2= (-4+4)^2+ (8+1)^2=0+81=81\\\\KL^2= (-4-2)^2+ (8-8)^2=36+0=36\\\\JL^2= (-4-2)^2+(8+1)^2=36+81=117](https://tex.z-dn.net/?f=JK%5E2%3D%20%28-4%2B4%29%5E2%2B%20%288%2B1%29%5E2%3D0%2B81%3D81%5C%5C%5C%5CKL%5E2%3D%20%28-4-2%29%5E2%2B%20%288-8%29%5E2%3D36%2B0%3D36%5C%5C%5C%5CJL%5E2%3D%20%28-4-2%29%5E2%2B%288%2B1%29%5E2%3D36%2B81%3D117)
As,
![\Rightarrow 117=81+36](https://tex.z-dn.net/?f=%5CRightarrow%20117%3D81%2B36)
![\Rightarrow JL^2=JK^2+KL^2](https://tex.z-dn.net/?f=%5CRightarrow%20JL%5E2%3DJK%5E2%2BKL%5E2)
![\Rightarrow \text{JKL is a right angle triangle}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Ctext%7BJKL%20is%20a%20right%20angle%20triangle%7D)
![\Rightarrow \angle K=90^{\circ}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cangle%20K%3D90%5E%7B%5Ccirc%7D)
Therefore, the vertex at K (-4, 8) is the orthocentre.
Answer:
936mm^2
Step-by-step explanation:
Surface area of cuboid 20 mm 8mm 11mm
Surface area of the cuboid=2(20×8+8×11+11×20)
=2(160+88+×220)
=2(468)
=936mm^2
So the answer is936mm^2
Angle B is 67 degrees. The definition of similar triangles gives us that the corresponding angles are equal. Angle E in the second triangle corresponds to angle A in the first triangle, ∠A=∠E=61 degrees. The sum of the internal angles of Triangle ABC is 180 degrees, so <span>∠B=180-61-52=67 degrees.</span>
Answer:
x = 55°, y = 70° and z = 125°
Step-by-step explanation:
Step 1 - Calculate ∠x:
As all angles on a line add up to 180°
125 + x = 180
x = 180 - 125
x = 55
Step 2 - Calculate ∠y:
As the triangle is an isosceles triangle, as evident by the two sides of equal length:
180 = y + 55 + 55
180 = y + 110
y = 180 - 110
y = 70
Step 3 - Calculate z:
180 - 55 = z
z = 125
Meaning that x = 55°, y = 70° and z = 125°
Hope this helps!
The answer is 4.76
all you have to do is subtract $20.00 -$15.24 and you have the answer