Question

find x such that SR containing points S(1,-2) and R(x,2) is perpindicular to TV containing points T(4,2) and V (6,7).

Answer 1

the value of x is -9 for SR to be perpendicular to TV.

Explanation:

To find the value of x such that line SR is perpendicular to line TV, you can use the fact that two lines are perpendicular when the product of their slopes is -1.

The slope of SR (m_SR) is (2 - (-2)) / (x - 1) = (4) / (x - 1).

The slope of TV (m_TV) is (7 - 2) / (6 - 4) = (5) / (2).

To make SR perpendicular to TV, the product of their slopes should be -1:

m_SR * m_TV = -1.

So, (4 / (x - 1)) * (5 / 2) = -1.

Now, you can solve for x:

(4 / (x - 1)) * (5 / 2) = -1

Multiplying both sides by (2(x - 1)) to eliminate fractions:

4 * 5 = -2(x - 1)

20 = -2(x - 1)

Now, divide by -2 to solve for x:

x - 1 = -10

x = -10 + 1

x = -9