Explanation: SV = VU 2x + 11 = 8x – step one 8x – 2x = eleven + step one 6x = twelve x = dos Uv = 8(2) – step one = 15

Explanation: Remember your circumcentre out of a good triangle are equidistant regarding vertices out-of an effective triangle. Assist A good(- cuatro, 2), B(- cuatro, – 4), C(0, – 4) become vertices of your own offered triangle and you will assist P(x,y) end up being the circumcentre of this triangle. Upcoming PA = PB = Desktop PA? = PB? = PC? PA? = PB? (x + 4)? + (y – 2)? = (x + 4)? + (y + 4)? x? + 8x + 16 + y? – 4y + 4 = x? + 8x + sixteen + y? + 8y + sixteen 12y = -12 y = -step one PB? = PC? (x + 4)? + (y + 4)? = (x – 0)? + (y + 4)? x? + 8x + 16 + y? + 8y + 16 = x? + y? + 8y + 16 8x = -sixteen x = -2 The brand new circumcenter was (-dos, -1)

Explanation: Recall the circumcentre out of a good triangle is actually equidistant regarding the vertices out-of an excellent triangle. Help D(step 3, 5), E(eight, 9), F(11, 5) end up being the vertices of your own given triangle and let P(x,y) be the circumcentre regarding the triangle. Then PD = PE = PF PD? = PE? = PF? PD? = PE? (x – 3)? + (y – 5)? = (x – 7)? + (y – 9)? x? – 6x + nine + y? – 10y + twenty five = x? – 14x + forty two + y? – 18y + 81 -6x + 14x – 10y + 18y = 130 – 34 8x + 8y = 96 x + y = a dozen – (i) PE? = PF? (x – 7)? + (y – 9)? = (x – 11)? + (y – 5)? x? – 14x + 49 + y? – 18y + 81 = x? – 22x + 121 + y? – 10y + twenty five -14x + 22x – 18y + 10y = 146 – 130 8x – 8y = sixteen x – y = 2 – (ii) Add (i) (ii) x + y + x – y = a dozen + 2 2x = fourteen x = seven Place x = eight in the (i) 7 + y = twelve y = 5 The new circumcenter try (seven, 5)

Explanation: NQ = NR = NS 2x + 1 = 4x – nine 4x – 2x = 10 2x = ten x = 5 NQ = 10 + 1 = eleven NS = 11

Explanation: NU = NV = NT -3x + 6 = -5x -3x + 5x = -6 2x = -6 x = -step three NT = -5(-3) = 15

Explanation: NZ = New york = NW 4x – 10 = 3x – step 1 x = nine NZ = 4(9) – 10 = thirty six https://datingranking.net/pl/willow-recenzja/ – 10 = twenty six NW = twenty six

Explanation: 5x – cuatro = 4x + 3 x = eight ?JGK = 4(7) + 3 = 30 meters?GJK = 180 – (30 + 90) = 180 – 121 = 59

Discover the coordinates of your centroid of your triangle wilt the brand new given vertices. Question nine. 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