4. Use slope and/or distance formula to show that quadrilateral DUST is a square. D(-1,7), U(7,1), S(1, –7), T(-7,–1)

Q: The distance from the point P(3, 1,0) and the line x = 3 – 6t y =1+ 3t z = 7t equals to Answer:

A:

Q: 8. Find the point (x. y) such that (1, 3) is the midpoint of the line segment connecting a. (x, y)…

A:

Q: For what values of the constants k and c does the line x- 3 ** =- lie in the plane x - y + 2z = c? O…

A: Given equation of   line  ;   x-32=y-2k=z+14plane;  x-y+2z=c key points 1)  given line lies in the…

Q: . Calculate the area of the triangle formed by the line 3x-7y+4 =0 , and the (ans.: 8/21) axes.

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 3) Let M be the midpoint of a line segment joining two points A(20, -1) and B (4, –9). Calculate the…

A:

Q: O Find the shortest distance from (1, 2, 3) to the line x = 3+t, y = 1 – t, z = 6 - 2t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. Show that the lines having the equations 4x- 3y + 12 = 0 and 8x 6y + 15 = 0 are parallel.

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Q: 4. Find the distance between the two points S(-5,-2) and T(-3,4).

A:

Q: 2. Suppose A, B,C, D e E³ are distinct points occurring in that order ong a straight line. a) Show…

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Q: a) Find the distance between the point P=(9, 1) and the line 3x+4y=6.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 3. If the slope of one of the pairs of lines represented by equation a³x² + 2hxy + b³y² = 0 is…

A:

Q: Find the distance d between the point M(5, 2, 4) and the line x- 8 y -2 Z-2 %D -8 -9 7.

A:

Q: For what value of k will the line kx + 5y = 2k be perpendicular to the line 2x - 3y = 1?

A:

Q: 4. What is the equation of a line parallel to the diameter of circle A, with a center at (-5,7) and…

A: Given query is to find the line which parallel to the given line.

Q: For what values of the constants k and c does the line x- 3 _ y-2 z+1 * = = 2 lie in the plane x - y…

A:

Q: If M(4, 3) is the midpoint of the line segment AB, and if A has coordinates (1, -1), find the…

A: M4, 3 is the midpoint of the line segment AB and the coordinates of A are 1, -1.

Q: 4. 3 2. 54 3-2 -1 1 2 4. -2 -3 -4 -5 -61 3.

A:

Q: 4. Find an equation for the line segment between P(3, -8,0) and Q(-1, 4, 2).

A: Our aim is to find the equation of line.

Q: Q)Suppose that one line is parallel y=13x+ 13 and passes through (15,7). Where does that line cross…

A: Given :  y=13x+ 13  compare with y = mx + c slope m = 13

Q: 4. Which of the following lines is parallel to y = 6x 18? 3x+6y=2 ○ 2x + 3y = −2 -6x -6x - 2y 2y =…

A:

Q: the distance from the point P(2,3) to the line -3y=-4x is : * 1/5 - 1/5 غير معرفة 1/25 17/5

A:

Q: Show that the lines of equations x=−1+t , y=−2+t, z=3t for t∈R and x=5+s, y=−8+2s, z=7s for ?∈ℝ are…

A:

Q: 23. The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y. O…

A: Given that the distance from a point 2,y to the line 4x+3y=0 isequal to 5. We need to find the value…

Q: 10. If M is the midpoint of the line AB where A has coordinates (- 6,5) and B has coordinates (4,3).…

A:

Q: What is the value of a if the point (a, – 1) is on the line 3x – 2y = 8? a =

A: We have to find the value of a.

Q: Find the shortest distance between the skewed lines. l1: = 1+ 2t, y = -1+t, z = 2+ 4t and l2: x= -2+…

A:

Q: 2. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 1) and K(10, 7). (8,…

A: To calculate the mid point of join of given points. To find the slope of the line perpendicular to…

Q: If m>0 and the points (m,3) and (1,m) lie on a line with slope m, then find m?

A: SLOPE OF A LINE PASSING THROUGH TWO POINTS   X1,Y1           AND   X2, Y2    IS…

Q: O Find the distance from the point (2, 1, 4) to the line r = (-t,6 – 2t, 8 – t).

A:

Q: Consider the line L(t)=(5,2t,5t-5) and the point P=(1,5,2). How far is P from the line L?

A:

Q: Find the shortest distance between the point Q(2, 0, 0) and the line segment joining the points…

A: Formula used: Distance between the point and a line is, D=PQ×uu Where u=P2-P1

Q: 4. In the xy-plane, the line.determined by the points (3, a) and (a, 12) passes through the origin.…

A:

Q: Find the point ( x, y) such that (1, 3) is the midpoint of the line segment connecting а. (х, у) and…

A: NOTE-Since you have posted a question with multiple sub-parts, we will solve first three subparts…

Q: 1. Which of the following lines is parallel to y = 4x 2?

A:

Q: What is the value of k such that the lines 3x+6ky=7 and 9kx+8y=15 will have the same positive slope?

A: 3x+6ky=7 and 9kx+8y=15

Q: If a line segment has endpoints A(2x + 7,4y) and B(4x + 3,- 2y), what are the coordinates of the…

A: A line segment has endpoints A2x+7, 4y and B4x+3, -2y

Q: 2- The distance d from the point R=(1,4,-3) to the line L: x=2+t,y%3-1-t Z- 3t is 4.43 False True

A:

Q: 5. Find the point of intersection of the following lines x = 4t +2, y = 3, z = -t +2 b. x = 2s +6, y…

A: Given query is to find the point of intersection of line a and line b.

Q: 16 4 2 -6 -4 -2 2 4 -2 -4

A: topic - relection of point about y=1 C'(2,4)

Q: Find the cоттоn points of the circles (x + 1)² + (y – 1)² = 5 and x² + y? = 1.

A: Common points of the circles simply means the point of intersection of the given circles.

Q: 7. Given that M4,6) is the mid-point of the line segment joining C(2, -3) and D, find the…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: 8. Find a line uniquely parallel to the line 3x-4y+12=0.

A:

Q: 10 X- 3y dA, where R is the parallelogram enclosed by the lines x - 3y = 0, x - 3y = 5, 8x - y = 5,…

A:

Q: Find k so that the line through (3, 2) and (k, 3) is a. parallel to 25x + 17y = 34, b. perpendicular…

A: We will be using the following concepts: Parallel lines have the same slope. The product of slope…

Q: B is the midpoint of line segment AC. Find x C 5X-6 3X +4 Ox = -5 O x 2 Ox = 5 Ox = 10

A: A line segment is a finite section of a straight line. A mid-point of a line segment is a point…

Q: 4) Find the point in which the line through the origin perpendicular to the plan 2x - y -z = 4 meets…

A:

Q: If M(6,8) is the midpoint of the line segment AB and if A has coordinates (2,3), fınd the…

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.