6.step one and you may six.3 Test
Explanation: SV = VU 2x + eleven = 8x – 1 8x – 2x = 11 + step 1 6x = several x = dos Ultraviolet = 8(2) – step one = fifteen
Explanation: Recall that the circumcentre out of a great triangle try equidistant throughout the vertices out-of good triangle. Help A(- 4, 2), B(- 4, – 4), C(0, – 4) function as vertices of the provided triangle and assist P(x,y) function as circumcentre of the triangle. Upcoming PA = PB = Desktop computer PA? = PB? = PC? PA? = PB? (x + 4)? + (y – 2)? = (x + 4)? + (y + 4)? x? + 8x + 16 + y? – 4y + 4 = x? + 8x + 16 + y? + 8y + sixteen 12y = -12 y = -step one PB? = PC? (x + 4)? + (y + 4)? = (x – 0)? + (y + 4)? x? + 8x + sixteen + y? + 8y + sixteen = x? + y? + 8y + sixteen 8x = -16 x = -2 The fresh circumcenter try (-2, -1)
Explanation: Recall that circumcentre regarding an effective triangle is equidistant in the vertices out-of a triangle. Help D(step 3, 5), E(eight, 9), F(11, 5) function as vertices of the given triangle and you can assist P(x,y) end up being the circumcentre from the triangle. Then PD = PE = PF PD? = PE? = PF? PD? = PE? (x – 3)? + (y – 5)? = (x – 7)? + (y – 9)? x? – 6x + nine + y? – 10y + 25 = x? – 14x + forty-two + y? – 18y + 81 -6x + 14x – 10y + 18y = 130 – 34 8x + 8y = 96 x + aplicaciones de citas para más de 60 adultos y = twelve – (i) PE? = PF? (x – 7)? + (y – 9)? = (x – 11)? + (y – 5)? x? – 14x + forty two + y? – 18y + 81 = x? – 22x + 121 + y? – 10y + 25 -14x + 22x – 18y + 10y = 146 – 130 8x – 8y = sixteen x – y = 2 – (ii) Include (i) (ii) x + y + x – y = 12 + 2 2x = fourteen x = seven Place x = 7 during the (i) eight + y = twelve y = 5 The circumcenter try (7, 5)
Explanation: NQ = NR = NS 2x + step one = 4x – 9 4x – 2x = ten 2x = 10 x = 5 NQ = 10 + step 1 = eleven NS = 11
Explanation: NU = NV = NT -3x + 6 = -5x -3x + 5x = -six 2x = -six x = -step three NT = -5(-3) = fifteen
Explanation: NZ = New york = NW 4x – ten = 3x – 1 x = 9 NZ = 4(9) – 10 = 36 – ten = twenty six NW = twenty six
Explanation: 5x – 4 = 4x + three times = seven ?JGK = 4(7) + step three = 31 meters?GJK = 180 – (31 + 90) = 180 – 121 = 59
Get the coordinates of centroid of triangle wilt the brand new considering vertices. Question 9. J(- step one, 2), K(5, 6), L(5, – 2)
Explanation: The slope of TU = \(\frac < 1> < 0>\) = -2 The slope of the perpendicular line is \(\frac < 1> < 2>\) The perpendicular line is y – 5 = \(\frac < 1> < 2>\)(x – 2) 2y – 10 = x – 2 x – 2y + 8 = 0 The slope of UV = \(\frac < 5> < 2>\) = 2 The slope of the perpendicular line is \(\frac < -1> < 2>\) The perpendicular line is y – 5 = \(\frac < -1> < 2>\)(x + 2) 2y – 10 = -x – 2 x + 2y – 8 = 0 equate both equations x – 2y + 8 = x + 2y – 8 -4y = -16 y = 4 x – 2(4) + 8 = 0 x = 0 So, the orthocenter is (0, 4) The orthocenter lies inside the triangle TUV