Explanation: QP = QR 6x = 3x + 9 3x = 9 x = step 3 QP = 6(3) = 18

6.step 1 and six.3 Quiz

Explanation: SV = VU 2x + eleven = 8x – step one 8x – 2x = 11 + step one 6x = twelve x = 2 Uv = 8(2) – step 1 = 15

Explanation: Remember that the circumcentre away from a triangle was equidistant regarding vertices off an effective triangle. Let An excellent(- 4, 2), B(- 4, – 4), C(0, – 4) be the vertices of provided triangle and you will assist P(x,y) end up being the circumcentre associated with triangle. Following PA = PB = Desktop PA? = PB? = PC? PA? = PB? (x + 4)? + (y – 2)? = (x + 4)? + (y + 4)? x? + 8x + sixteen + y? – 4y + cuatro = x? + 8x + 16 + y? + 8y + 16 12y = -twelve y = -1 PB? = PC? (x + 4)? + (y + 4)? = (x – 0)? + (y + 4)? x? + 8x + sixteen + y? + 8y + 16 = x? + y? + 8y + 16 8x = -16 x = -2 The new circumcenter try (-2, -1)

Explanation: Remember the circumcentre off a great triangle try equidistant on vertices of a beneficial triangle. Help D(step 3, 5), E(7, 9), F(eleven, 5) function as vertices of one’s provided triangle and you can help P(x,y) end up being the circumcentre on the triangle. Following PD = PE = PF PD? = PE? = PF? PD? = PE? (x – 3)? + (y – 5)? = (x – 7)? + (y – 9)? x? – 6x + 9 + 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 = 16 x – y = dos – (ii) Put (i) (ii) x + y + x – y = a dozen + dos 2x = fourteen x = 7 Lay x = seven when you look at the (i) eight + y = 12 y = 5 The new circumcenter are (7, 5)

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

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

Explanation: NZ = Ny = NW 4x – ten = 3x – step 1 x = nine NZ = 4(9) – 10 = 36 – 10 = twenty six NW = twenty six

Explanation: 5x – cuatro = 4x + three times = eight ?JGK = 4(7) + step three = 29 meters?GJK = 180 – (29 + 90) = 180 – 121 = 59

Get the coordinates of your own centroid of your own triangle wilt the brand new considering vertices. Question nine. J(- step 1, 2), K(5, 6), L(5, – 2)

Explanation: The slope of TU = citas en línea para estudiantes universitarios \(\frac < 1> < 0>\) = -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