Find b such that the points A(2,b),B(5,5)and C(-6,0) are the vertices of right angled  with angle < BAC = 90 degree.
2 answers:
The <BAC angle isn't a perfect right angle because the image was a photo
<em><u>If this helped, please consider picking this answer as the Brainliest Answer. Thank you!</u></em>
Answer:
- b = -3 or b = 8
Step-by-step explanation:
We know that the perpendicular lines have negative-reciprocal slopes.
In other words, their product is - 1.
<u>Find the slopes of AB and AC:</u>
- m(AB) = (5 - b)/(5 - 2) = (5 - b) / 3
- m(AC) = (0 - b)/(- 6 - 2) = - b / - 8 = b/8
<u>Find the the product of slopes and solve for b:</u>
- (5 - b)/3 * b/8 = - 1
- b(b - 5)/24 = 1
- b(b - 5) = 24
- b² - 5b - 24 = 0
- b² - 8b + 3b - 24 = 0
- b(b - 8) + 3(b - 8) = 0
- (b + 3)(b - 8) = 0
- b = - 3 or b = 8
You might be interested in
The statements and reasons why the given statements are true are presented in the following two column proofs;
Question 1
Given: 9·(x + 6) - 41 = 75
Statement Reason
S1. 9·(x + 6) - 41 = 75 R1. <u>Given</u>
S2. 9·(x + 6) = 116 R2. <u>Addition property</u>
S3. <u>9·x + 54 = 116 </u> R3. Distributive property
S4. 9·x = 62 R4. <u>Subtraction property</u>
S5.
R5. <u>Division property of equality</u>
Question 2.
Statement Reason
S1. m∠A + m∠B = m∠D R1. Given
S2. ∠C and ∠D form a Linear Pair R2. Definition of linear pair
S3. ∠C and ∠D are supplementary R3. <u>Linear pair ∠s are supplementary</u>
S4. <u>∠C + ∠D = 180° </u> R4. Definition of supplementary
S5. m∠C + m∠A + m∠B = 180° R5. <u>Substitution property</u>
Question 3.
Statement Reason
S1. ∠BDA ≅ ∠A R1. Given
S2. ∠BDA ≅ ∠CDE R2. <u>Vertical angle theorem</u>
S3. ∠CDE ≅ ∠A R3. Transitive property of congruency
S4. m∠CDE = m∠A R4. <u>Definition of congruency</u>
S5. <u>(13·x + 20)° = (14·x + 15)°</u> R5. Substitution Property of Equality
S6. 14·x° = 13·x + 5° R6. <u>Subtraction property</u>
S7. x = 5 R7. Subtraction property
Learn more here: