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

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

six.1 and you will 6.3 Test

Explanation: SV = VU 2x + eleven = 8x – 1 8x – 2x = eleven + step 1 6x = several x = 2 Uv = 8(2) – step one = fifteen

Explanation: Keep in mind that the circumcentre of a triangle is actually equidistant from the vertices from a triangle. Assist A good(- 4, 2), B(- cuatro, – 4), C(0, – 4) end up being the vertices of your own considering triangle and you may assist P(x,y) become circumcentre regarding the triangle. Up coming PA = PB = Desktop PA? = PB? = PC? PA? = PB? (x + 4)? + (y – 2)? = (x + 4)? + (y + 4)? x? + 8x + sixteen + y? – 4y + cuatro = x? + 8x + sixteen + y? + 8y + 16 12y = -several y = -step 1 PB? = PC? (x + 4)? + (y + 4)? = (x – 0)? + (y + 4)? x? + 8x + sixteen + y? + 8y + 16 = x? + y? + 8y + 16 8x = -16 x = -dos The newest circumcenter was (-2, -1)

Explanation: Recall that the circumcentre away from a triangle is actually equidistant on vertices from an effective triangle. Assist D(step 3, 5), E(7, 9), F(11, 5) be the vertices of the provided triangle and you may let P(x,y) function as circumcentre in the triangle. Upcoming 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 + 44 + y? – 18y + 81 -6x + 14x – 10y + 18y = 130 – 34 8x + 8y = 96 x + y = 12 – (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) Add (i) (ii) x + y + x – y = a dozen + dos 2x = fourteen x = eight Lay x = seven into the (i) eight + y = 12 y = 5 The fresh circumcenter was (eight, 5)

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

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

Explanation: NZ = New york = NW 4x – 10 = 3x – step one x = 9 NZ = 4(9) – ten = 36 – ten = twenty-six NW = twenty-six

Explanation: 5x – cuatro = 4x + 3 x = eight ?JGK = 4(7) + 3 = 30 m?GJK = 180 – (29 + 90) im Freien-Dating-Seite = 180 – 121 = 59

Discover the coordinates of the centroid of one’s triangle wilt the brand new considering vertices. Question nine. J(- step 1, 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

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