Median and Midsegment of a Triangle

9 Find the point that partitions the indicated segment with the two given endpoints with the given ratio. 10. A(-9, 3), BCI, 8); 2:3 AB 11. Age B(4, 7): 1:3 BA 10 4<4,-12> 41,-3> 7<10,57 <4,27 Components: 410,57 Point: (+5,5) Components: <4, - 127 Point: (5, 4) 12. A(4 9), B6-5, -3); 23 AB 13. Find the coordinates of point P that lies of the way 34-9,-12> 4-38,-4,87 on the direct line segment AB, where 1(-2, ⅔ 46,37 <4,2› Components: 41, -12) Point: (-4, 4, 2) Point: (2, 7) = 75 pt / ox 7 70 Quiz - Median and Midsegment of a Triangle Name: Partitioning a Line Segment & Circle Equations Date: Point G is the centroid of AABC. Use the given information to give the value of x. 1. BG - 4x + 5 and DG - 3x 2 2.5 6x = 4x+5 2x =5 2. EG - 2x- 8 and EC - 3x + 3 4 1.9 61-24,71+3 3. GF - 3x - 2 and AG = 3x 4 20 6x -4 = 5ª 4. What is the length of AF? 330 x =4 Refer to the triangle at the right for 4 - 8. D. E, and F are midpoints of their respective segments. 5. IFAC - 16, and EF - (3x - 4), find the value of x. - 8 = 4 6. If DE - 3x + 1, and CB - 10x - 6, find FB. 473 6x+2 = 10x- 6 x== 7. EF -x-1,AC - 3x - 7, find BF. 8 2x-2 = 34-7 x=9 8. DE - 5, AC - 14, 4B - 9, find the perimeter of MCB. 42. 3 18 9. I(mZBFE - 75°, find mLBCA. 75° (4, 7) (1,3) (-2, -1) 6 14. C is the center of the circle shown at the right. What is the equation of circle C? A. (x - 1)ª + (y - 3)ª = 25 B. (x + 1)? + (y + 3)ª = 25 C. (x - 1)? + (y - 3)ª = 100 D. (x + 1)? + Cy + 3)ª = 100 2. Answer: Write the equation of the circle: 15. The center is at (-4,5), having a radius of 12. 16. The endpoints of the diameter are (4, 5) and (-2, 7). С (8,6) 32+ 1* = 10 Equation: (x-1) '+ (y-)"= 10 equation: (x+4) '+(y-5)25144 17. The center is at the origin, containing the point (4, 2). 1o 18. Graph the circle with the equation (x + 2)ª + (y - 3)ª = 16. Center: (-2, 3 / Radius:" 4 Identify 4 points on the circle 1(-2,7) 1(-2, ~1) 1(-6,3) '(7,3) equation: x=+ y ₴ 20 19. Identify the center and radius of the circle having the given cquation: (x + 5)? + (y - 6)ª = 49. Center: '(-5, 6) Radius? 7 20. Write the equation of the circle shown on the graph below. 2 equation: (x - 3) + (y+4)*= 36 Quiz - Median and Midsegment of a Triangle Name: Partitioning a Line Segment & Circle Equations Date: Point G is the centroid of ABC. Use the given information to give the value of x. 1. BG - 4x + 9 and DG - 3x 2_4.5 6x = 4x +9 2. EG - 2x - 8 and EC - 3x + 9 2_ 11 6x-24=3x+9 3. GF - 3x - 6 and AG - 4x 12. 24 4. What is the length of AF? 6 3- 6x-12 = 4x x = 6 36° Refer to the triangle at the right for 4 - 8. D, E, and F are midpoints of their respoctive segments. 5. If AC - 28, and EF = (3x - 4), find the value of x. 14 = 6 6. If DE = 3x + 1, and CB = 7x - 3, find FB. 16 3 6222 = 71-3 X=5 7. ER =x- 1, AC - 3x - 10, find EF. 2x-2 = 3x - 10 7 3 x = 8 8. DE= 8, AC - 18, 4E = 9, find the perimeter of MACB. 52. 16 9. If mZBFE = 65°, find m ZBCA. 65 ° 3 Find the point that partitions the indicated segment with the two given endpoints with the given ratio. 10. A(-6, 3), B(-1, 13); 2:3 AB 11. AlS $ 45,107 <2, 4) Components: : 45,107 Point: (-4, 7) 12. A(1, 11), B(-5, -3); 2:3 AB 54-6-147 4-2-4-5.67 Components: <-6,~ 14> Point: (-1.4,5,4) 18, 3); 1:3 BA <-12, -8> <-3,-27 Comporent - 12,-87 Point: (15, 4) 13. Find the coordinates of point P that lies; of the way on the direct line segment AB, where 1(-2, 5), B(1, 11). <3,67 <2,47 Point (0, 9) 6 2 14. C is the center of the circle shown at the right. What is the equation of circle C? A. (x + 1)2 + (y + 3)? = 25 B. (x - 1)2 + (y - 3)? = 25 C. (x - 1)2 + (y - 3)* = 100 D. (x + 1) + (y + 3)? = 100 2 Answer: Write the equation of the circle: 15. The center is at (-2,7), having a radius of 9. (4, (1,3), (-2, -1) 16. The endpoints of the diameter are (-4,7) and (2, 3). C (-1,5 ) 513 equalion: (X+1) + (y-5)"=13 equation: (8+2) + (y-7)*=81 17. The center is at the origin, containing the point (6, 2)- 18. Graph the circle with the equation (x - 2)? + (y + 3)? = 25. Center? (2, -3) Radius: Identify 4 points on the circle. (2, 3) (7, -3) / (-3,-3) (2,-8. equation: x°+ y 2=40 19. Identify the center and radius of the circle having the given equation: (x - 6)ª + (y + 1)? = 9. Center: (6,-1) Radius: 3 20. Write the equation of the circle shown on the graph below. equation: (x+4) + (y-3) *÷25